No links please Chapter name : Vector Q14 ABCD is a parallelogram ; p - Maths - Vector Algebra

Question

No links please

Chapter name :
Vector

Q14 ABCD is a parallelogram ; p and Q are the mid-points of the
sides A B   and   D C   respectively Show that DP
  and   BQ trisect A C   and are trisected by A C

Lovina Kansal · Accepted Answer

Dear student
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Taking O as origin, let the position vector B and D be b→ and d→ respectively
Then position vector of C is b→+d→Since P and Q are the mid points of AB and CD respectively
 So, position vectorsof P and Q are b→2 and b→2+d→ respectively
The position vector of a point dividing AC in the ratio 1:2 is1
b→+d→+2
0→1+2=b→+d→3Also, the position vector of the point dividing DP in the ratio 2:1 is2b→2+1
d→2+1=b→+d→3Thus, the point of trisection of AC coincides with the point of trisection of DP
Hence, DP cuts the diagonals AC in its point of trisection, which is also the point of trisection of DP
Similalrly, BQ cuts the diagonal AC in its point oftrisection, which is also the  point of trisection of BQ
Regards

No links please Chapter name : Vector Q14. ABCD is a parallelogram ; p and Q are the mid-points of the sides A B and D C respectively. Show that DP and BQ trisect A C and are trisected by A C .

No links please

Chapter name :
Vector

Q14. ABCD is a parallelogram ; p and Q are the mid-points of the sides $A B and D C$ respectively. Show that $DP and BQ$ trisect $A C$ and are trisected by $A C$ .