Question

(Q) The position vector of p and q are respectively a and b if R is a point on PQ such that PR=5PQ,then the position vector of R is

1) 5b-4a 2)5b+4a
3)4b-5a 4)4b+5a​

Answer 1

Given:

$\quad\quad$• Position vector of P = $\mathtt{\vec{a}}$

$\quad\quad$• Position vector of Q = $\mathtt{\vec{b}}$

To find: The position vector of R.

Given, $\mathtt{\vec{PR}=5\:\vec{PQ}}$

$\Rightarrow\mathtt{P.v.\:of\:R - P.v.\:of\:P = 5\:(P.v.\:of\:Q - P.v.\:of\:P)}$

$\Rightarrow\mathtt{Position\:vector\:of\:R - \vec{a}=5\:(\vec{b}-\vec{a})}$

$\Rightarrow\mathtt{Position\:vector\:of\:R=5\:\vec{b}-5\:\vec{a}+\vec{a}}$

$\Rightarrow\mathtt{Position\:vector\:of\:R=5\:\vec{b}-4\:\vec{a}}$

∴ position vector of R is $\mathtt{(5\:\vec{b}-4\:\vec{a})}$

So, Option (1) is correct.

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