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Mitali

Subject: Maths, asked on 14/4/18

Please give an.easy solution
ILLUSTRATION 1 Let ABC be a triangle having its centroid at G. If S is any point in the plane of the triangle, then $S \vec{A} + S \vec{B} + S \vec{C} =$
(a) $S \vec{G}$
(b) 2 $S \vec{G}$
(c) $3 S \vec{G}$
(d) $\vec{0}$
Ans. (c)

Sangeeta Jha

Subject: Maths, asked on 2/4/18

Solve this:
Q25. Let a, b and c be three non-zero vectors such that no two of them are collinear and (a × b) × c = $\frac{1}{3}$ |b|| c| a. If $θ$ is the angle between vectors b and c, then a value of sin $θ$ is

(a) $\frac{2 \sqrt{2}}{3}$ (b) $\frac{- \sqrt{2}}{3}$

(c) $\frac{2}{3}$ (d) $\frac{- 2 \sqrt{3}}{3}$

Yokeshwar Yokananthan

Subject: Maths, asked on 1/4/18

let a= i+4j+2k , b= 3i-2j+7k and c=2i-j+4K which of the following is representing a vector p which is perpendicular to both a and b and also whose scalar product with c would be p.c=18

Jassimrat Kaur

Subject: Maths, asked on 30/3/18

Please solve example 20

Q. EXAMPLE 20. If $\vec{a}, \vec{b,} \vec{c}$ are three non - zero vectors which are pairwise non-collinear. If $\vec{a} + 3 \vec{b}$ is collinear $\vec{c} and \vec{b} + 2 \vec{c} is collinear with \vec{a} then \vec{a} + 3 \vec{b} + 6 \vec{c}$ is :

$(a) \vec{c} (b) \vec{0} (c) \vec{a} + \vec{c} (d) \vec{a}$
[ AIEEE 2011 ]

Souptik

Subject: Maths, asked on 29/3/18

$Q 1 . T h e s l o p e o f t h e l i n e t o u c h i n g b o t h t h e p a r a b o l a s y^{2} = 4 x a n d x^{2} = - 32 y i s (a) \frac{1}{2} (b) \frac{3}{2} (c) \frac{1}{8} (d) \frac{2}{3} Q 2 . T h e \tan g e n t a t (1, 7) t o t h e c u r v e s x^{2} = y - 6 x t o u c h t h e c i r c l e x^{2} + y^{2} + 16 x + 12 y + x = 0 a t (a) (6, 7) (b) (- 6, 7) (c) (6, - 7) (d) (- 6, - 7)$

Chaitanya Kapoor

Subject: Maths, asked on 26/3/18

Solve this:

Q. Which one of the following vectors of magnitude $\sqrt{51}$ makes equal angles with three vectors
$\vec{a} = \frac{\hat{i} - 2 \hat{j} + 2 \hat{k}}{3}, \vec{b} = \frac{- 4 \hat{i} - 3 \hat{k}}{5} a n d \vec{c} = \hat{j}$ ?
$(a) 5 \hat{i} - \hat{j} - 5 \hat{k} (b) 5 \hat{i} + \hat{j} + 5 \hat{k} (c) - 5 \hat{i} - \hat{j} + 5 \hat{k} (d) 5 \hat{i} + 5 \hat{j} - 5 \hat{k}$

Chaitanya Kapoor

Subject: Maths, asked on 26/3/18

$Q 2 . I f \vec{a}, \vec{b}, \vec{c} a r e t h e p o s i t i o n v e c t o r s o f c o r n e r s A, B, C o f a p a r a l l e \log r a m A B C D, t h e n w h a t i s t h e p o s i t i o n v e c t o r o f t h e c o r n e r D ? (a) \vec{a} + \vec{b} + \vec{c} (b) \vec{a} + \vec{b} - \vec{c} (c) \vec{a} - \vec{b} + \vec{c} (d) - \vec{a} + \vec{b} - \vec{c}$

Chaitanya Kapoor

Subject: Maths, asked on 26/3/18

116. $I f |\overset{⇀}{a}| = \sqrt{2}, |\overset{⇀}{b}| = \sqrt{3} a n d |\overset{⇀}{a} + \overset{⇀}{b}| = \sqrt{6}, t h e n w h a t i s |\overset{⇀}{a} - \overset{⇀}{b}| e q u a l t o ?$
1. 1 2. 2 3. 3 4. 4

Hrushikesh Badgujar

Subject: Maths, asked on 26/3/18

Q . 21 solution

$Q . 21 T h e v e c t o r s \vec{A B} = 3 \hat{i} - 2 \hat{j} + 2 \hat{k} a n d \vec{B C} = - \hat{i} - 2 \hat{k} a r e t h e a d j a c e n t s i d e s o f a p a r a l l e \log r a m . T h e a n g l e b e t w e e n i t s d i a g o n a l s i s (A) \frac{π}{4} (B) \frac{π}{3} (C) \frac{3 π}{4} (D) \frac{2 π}{3}$

Hrushikesh Badgujar

Subject: Maths, asked on 26/3/18

The cosine of the angle between vectors p and q such that 2p+q=i+j , p+2q=i-j is

Shubhrajyoti Ghosh

Subject: Maths, asked on 23/3/18

Solve this :

(i) If the sum of two unit vectors is a unit vector then show that the magnitude of their difference is $\sqrt{3} .$

Manjiri Gokhale

Subject: Maths, asked on 21/3/18

Question 5

Manjiri Gokhale

Subject: Maths, asked on 21/3/18

If a,b,c are unit vectors prove that |a-b|^2 + |b-c|^2 + |c-a|^2 ?9

Tks Arunachalam

Subject: Maths, asked on 20/3/18

$Q . I f \vec{a} \times \vec{b} = \vec{a} \times \vec{c}, \vec{a} \neq 0, \vec{b} \neq \vec{c}, s h o w t h a t \vec{b} = \vec{c} + t \vec{a} f o r s o m e s c a l a r' t' .$ Given: a→ × b→ = a→ × c→, a→ ≠ 0, b→ ≠ c→To prove: b→ = c→ + ta→ for some scalar 't'Given: a→ × b→ = a→ × c→, a→ ≠ 0, b→ ≠ c→To prove: b→ = c→ + ta→ for some scalar 't'

Tks Arunachalam

Subject: Maths, asked on 20/3/18

$Q . I f \vec{a} = 2 \hat{i} + 2 \hat{j} + \hat{k}, \vec{a} \cdot \vec{b} = 14, \vec{a} \times \vec{b} = 3 \hat{i} + \hat{j} - 8 \hat{k} . F i n d \vec{b} .$

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