Question

Position vector of the point which divides the join of vectors 3a-2b and 2a-3b in ratio 2:1

Answer 1

Answer:

$\frac{7a-8b}{3}$

Step-by-step explanation:

Since, when a points R divides a line segment having endpoints P and Q in the ratio m : n,

And, the position vector of P is $\overrightarrow{OP}$ and the position vector of Q is $\overrightarrow{OQ}$,

Then, the position vector of R is,

$\frac{m(\overrightarrow{OQ})+ n(\overrightarrow{OP})}{m+n}$

Here, $\overrightarrow{OP}=3a-2b$

$\overrightarrow{OP}=2a-3b$

m = 2 and n = 1,

Thus, the position vector of the point that divides the given points,

$=\frac{2\times (2a-3b)+ 1\times (3a-2b)}{2+1}$

$=\frac{4a-6b+3a-2b}{3}$

$=\frac{7a-8b}{3}$

Answer 2

Answer:

Step-by-step explanation:
The given vectors are 2a-3b and a+b in the ratio 3:1.

.. The position vector of the required point c which divides the join of the given vectors a and b is
C= (mx+ny)/m+n
={3(2a-3b)+1(a+b)}/3+1
=(6a-9b+a+b)/4
=(7a+8b)/4