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find the distance of the point (1,-2,3) from the plane x-y+z=5 measured along a line parellel to x/2=y/3=z/-6
find the image of point (1,2,3) in the plane 3x+2y-z=8
Find distance of the point (-2,3,-4) from the line (x+2)/3=(2y+3)/4=(3z+4)/5, measured parallel to the plane 4x+12y-3z+1=0
find the image of the point ( 1,6,3) inthe line x/1 = y-1/2 = z-2/3. Also write the equation of the line joining the given point and its image and find the length of the segment joining the given point and its image.
Show that the lines :
(x-1) /2 = (y-2) /3 = (z-3) /4 and (x-4) /5 = (y-1) 2 = z
intersect. find their point of intersection.
Find the distance of the point (a,b,c) from x-axis?
If A is a square matrix of order 3 such that |adj A|=225,find |A'|
Find the coordinates of the foot of the perpendicular from the point (2,3,-8) to the line (4-x)/2 = y/6 = (1-z)/3. Also find the perpendicular distance from the given point to the given line.
Find the coordinates of the point where the line through (3,-4,-5) and (2,-3,1) crosses the plane 2x + y + z = 7
Find the equation of the plane containing the lines--
r = i + j + u(i + 2j - k) and r = i + j + k(-i + j - 2k)
Find the distance of this plane from the origin and also from the point (1,1,1)
Q1. Find the equation of the plane which contains two parallel lines given by
(x-3) = (y+2) / (-4)= z/5 and (x-4) =(y-3) /(-4) =(z-2) / 5
Find the equation of the plane passing through the point P(1,1,1,) and containing the line r=(-3i+j+5k) + A(3i-j-5k). Also show that the plane contains the line r=(-i+2j+5k) + B(i-2j-5k).
Find the length and foot of the perpendicular from the point (1,1,2) to the plane r.(2i-2j+4k) +5=0?
A line makes angles alpha beeta gama and delta with the diagnols of a cube, prove
cos2 alpha+ cos2 beeta+cos2 gama+cos2 delta = 4/3.refer to example number 26th of ncert page 494.is there any easy way of solving this question. i think it is very important from boards point of view. please help
find the distance of point (2,3,4) from the plane 3x + 2y + 2z + 5 = 0 measured parallel to the line x+3/3=y-2/6=z/2
cos2a + cos2b + cos2c + cos2d =4/3
find cartesian eqn & vector eqn of the planes passing thru the intersection of the planes r(2i+6j)+12=0 and r(3i-j+4k)=0 which is at unit distance from origin
find the equation of the plane whick contains the line of intersection of the planes vector r.(i+2j+3k)-4=0 ,vector r.(2i+j-k)+5=0 and which is perpendicular to the plane vector r.(5i+3j-6k)+8=0.
Q.1. find the image of the point having position vector i^ +3j^ +4k^ in the plane
r--> . (2i^ -j^+ k^) + 3 = 0.
find shortest distance between the line :
x - 8/ 3 = y + 19/ -16 = z - 10/ 7 and x - 15/ 3 = y - 29 /8 = z - 5 / -5
Find the equation of the line passing through the point (-1,3,-2) and perpendicular to the lines x/1 =y/2=z/3 and x+2/5 = y-1/2= z+1/5
Find the distance of the point (3,4,5) from the plane x+y+z= 2 measured parallel to line 2x = y = z.............answer it fast
find the point on the line x+2/3=y+1/2=z-3/2 at a distance 3root2 from the point (1,2,3)
SHOW THAT THE POINTS (0,-1,-1),(4,5,1),(3,9,4) AND (-4,4,4) ARE COPLANAR.ALSO FIND THE EQUATION OF THE LINE CONTAINING THEM.
show that the lines r=(i+j-k)+ (3i-j) and r= (4i-k)+ u(2i+3k) intersect. also find their point of intersecion.
find the equation of plane passing through the points (3,4,1) and (0,1,0) and parallel to the line (x+3)/2=(y-3)/7=(z-2)/5
A line makes angles alpha ,beta,gamma and delta with diagonals of ther cube,prove that - cos ^ 2 alpha + cos ^ 2 beta + cos ^ 2 gamma + cos ^ 2 delta = 4 / 3
find the direction cosines of the lines connected by the relations :l+m+n=0 and 2lm+2ln-mn=0?
find the equation of the line passing through the point P(4,6,2) and the point of the intersection of the line x-1/3=y/2=z+1/7 and the plane x+y-z=8. Plz help me out with this question...
what is the difference between direction cosines and direction ratios??
What is the cosine of the angle which the vector √2 i + j + k makes with y-axis
Sir/Madam
In the problem ,Find the value of lambda Such that the line (X-2)/9 = Y-1/(lambda) = (Z+3)/-6 is perpendicular to the plane
3X-Y-2Z=7. (ans Lambda = - 3)(since line is perpendicular to the plane & parallel to its normal).How do we find the equation of the normal to the given Plane?
Find equation of plane passing through the point (-1,3,2) and perpendicular to each of the planes x+2y+3z=5 and 3x+3y+z=0.
Show that four points (0,-1,-1) (4,5,1) (3,9,4) (-4,4,4) are coplanar. Also find the equation of the plane containing them.
find the equation of the plane passing through the line of intersection of the planes r. ( i + 3j) -6 =0 and r. ( 3i - j - 4k ) =0, whose perpendicular distance from origin is unity.
The cartisian equation of a line arc 6x-2=3y+1=2z-2.Find a)The direction ratio of the line ?
b)Cartisian and vector equations of the line parallel to this line and passing through the point (2,-1,-1).
find the foot of the perpendicular from P(1,2,3) on the line x-6/3 = y-7/2=z-7/-2
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Syllabus
find the distance of the point (1,-2,3) from the plane x-y+z=5 measured along a line parellel to x/2=y/3=z/-6
find the image of point (1,2,3) in the plane 3x+2y-z=8
Find distance of the point (-2,3,-4) from the line (x+2)/3=(2y+3)/4=(3z+4)/5, measured parallel to the plane 4x+12y-3z+1=0
find the image of the point ( 1,6,3) inthe line x/1 = y-1/2 = z-2/3. Also write the equation of the line joining the given point and its image and find the length of the segment joining the given point and its image.
Show that the lines :
(x-1) /2 = (y-2) /3 = (z-3) /4 and (x-4) /5 = (y-1) 2 = z
intersect. find their point of intersection.
Find the distance of the point (a,b,c) from x-axis?
If A is a square matrix of order 3 such that |adj A|=225,find |A'|
Find the coordinates of the foot of the perpendicular from the point (2,3,-8) to the line (4-x)/2 = y/6 = (1-z)/3. Also find the perpendicular distance from the given point to the given line.
Find the coordinates of the point where the line through (3,-4,-5) and (2,-3,1) crosses the plane 2x + y + z = 7
Find the equation of the plane containing the lines--
r = i + j + u(i + 2j - k) and r = i + j + k(-i + j - 2k)
Find the distance of this plane from the origin and also from the point (1,1,1)
Q1. Find the equation of the plane which contains two parallel lines given by
(x-3) = (y+2) / (-4)= z/5 and (x-4) =(y-3) /(-4) =(z-2) / 5
Find the equation of the plane passing through the point P(1,1,1,) and containing the line r=(-3i+j+5k) + A(3i-j-5k). Also show that the plane contains the line r=(-i+2j+5k) + B(i-2j-5k).
Find the length and foot of the perpendicular from the point (1,1,2) to the plane r.(2i-2j+4k) +5=0?
A line makes angles alpha beeta gama and delta with the diagnols of a cube, prove
cos2 alpha+ cos2 beeta+cos2 gama+cos2 delta = 4/3.refer to example number 26th of ncert page 494.is there any easy way of solving this question. i think it is very important from boards point of view. please help
find the distance of point (2,3,4) from the plane 3x + 2y + 2z + 5 = 0 measured parallel to the line x+3/3=y-2/6=z/2
cos2a + cos2b + cos2c + cos2d =4/3
find cartesian eqn & vector eqn of the planes passing thru the intersection of the planes r(2i+6j)+12=0 and r(3i-j+4k)=0 which is at unit distance from origin
find the equation of the plane whick contains the line of intersection of the planes vector r.(i+2j+3k)-4=0 ,vector r.(2i+j-k)+5=0 and which is perpendicular to the plane vector r.(5i+3j-6k)+8=0.
Q.1. find the image of the point having position vector i^ +3j^ +4k^ in the plane
r--> . (2i^ -j^+ k^) + 3 = 0.
find shortest distance between the line :
x - 8/ 3 = y + 19/ -16 = z - 10/ 7 and x - 15/ 3 = y - 29 /8 = z - 5 / -5
Find the equation of the line passing through the point (-1,3,-2) and perpendicular to the lines x/1 =y/2=z/3 and x+2/5 = y-1/2= z+1/5
(x-3)/3. = (y+4)/2. = (z-1)/1
and
(x+1)/3. = (y-2)/2. = (z)/1
Find the distance of the point (3,4,5) from the plane x+y+z= 2 measured parallel to line 2x = y = z.............answer it fast
find the point on the line x+2/3=y+1/2=z-3/2 at a distance 3root2 from the point (1,2,3)
SHOW THAT THE POINTS (0,-1,-1),(4,5,1),(3,9,4) AND (-4,4,4) ARE COPLANAR.ALSO FIND THE EQUATION OF THE LINE CONTAINING THEM.
show that the lines r=(i+j-k)+ (3i-j) and r= (4i-k)+ u(2i+3k) intersect. also find their point of intersecion.
find the equation of plane passing through the points (3,4,1) and (0,1,0) and parallel to the line (x+3)/2=(y-3)/7=(z-2)/5
A line makes angles alpha ,beta,gamma and delta with diagonals of ther cube,prove that - cos ^ 2 alpha + cos ^ 2 beta + cos ^ 2 gamma + cos ^ 2 delta = 4 / 3
find the direction cosines of the lines connected by the relations :l+m+n=0 and 2lm+2ln-mn=0?
find the equation of the line passing through the point P(4,6,2) and the point of the intersection of the line x-1/3=y/2=z+1/7 and the plane x+y-z=8. Plz help me out with this question...
what is the difference between direction cosines and direction ratios??
What is the cosine of the angle which the vector √2 i + j + k makes with y-axis
Sir/Madam
In the problem ,Find the value of lambda Such that the line (X-2)/9 = Y-1/(lambda) = (Z+3)/-6 is perpendicular to the plane
3X-Y-2Z=7. (ans Lambda = - 3)(since line is perpendicular to the plane & parallel to its normal).How do we find the equation of the normal to the given Plane?
x+5/1=y+3/4=z-6/-9.Also write down the coordinates of the foot of the perpendicuar from P to the line
Find equation of plane passing through the point (-1,3,2) and perpendicular to each of the planes x+2y+3z=5 and 3x+3y+z=0.
Show that four points (0,-1,-1) (4,5,1) (3,9,4) (-4,4,4) are coplanar. Also find the equation of the plane containing them.
find the equation of the plane passing through the line of intersection of the planes r. ( i + 3j) -6 =0 and r. ( 3i - j - 4k ) =0, whose perpendicular distance from origin is unity.
The cartisian equation of a line arc 6x-2=3y+1=2z-2.Find
a)The direction ratio of the line ?
b)Cartisian and vector equations of the line parallel to this line and passing through the point (2,-1,-1).
find the foot of the perpendicular from P(1,2,3) on the line x-6/3 = y-7/2=z-7/-2