If the position vector of a point A is a + 2b | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the position vector of point $A$ be $\vec{OA} = a + 2b$.Let the position vector of point $P$ be $\vec{OP} = a$.Let the position vector of poin

Vedclass · Accepted Answer

$a - 3b$

Vedclass · Answer

(C) Let the position vector of point $A$ be $\vec{OA} = a + 2b$.Let the position vector of point $P$ be $\vec{OP} = a$.Let the position vector of point $B$ be $\vec{OB} = x$.Since $P$ divides $AB$ in the ratio $2:3$,by the section formula:$\vec{OP} = \frac{2(\vec{OB}) + 3(\vec{OA})}{2 + 3}$$a = \frac{2x + 3(a + 2b)}{5}$$5a = 2x + 3a + 6b$$2x = 5a - 3a - 6b$$2x = 2a - 6b$$x = a - 3b$Therefore,the position vector of $B$ is $a - 3b$.

If the position vector of a point $A$ is $a + 2b$ and a point $P$ divides $AB$ in the ratio $2:3$,where the position vector of $P$ is $a$,then the position vector of $B$ is:

Similar Questions

Given that $\vec{a} \cdot \vec{b} = 0$ and $\vec{a} \times \vec{b} = \vec{0}$. What can you conclude about the vectors $\vec{a}$ and $\vec{b}$?

Let $u$ and $v$ be two vectors. Then $|u-v|=||u|-|v||$ if and only if

Find the centroid of the triangle whose vertices are $i + 2j, 2i + j, i + j + k$.

In the given figure,which of the vectors are collinear?

$A, B, C, D$ are any four points. If $E$ and $F$ are midpoints of $AC$ and $BD$ respectively, then $\vec{AB} + \vec{CB} + \vec{CD} + \vec{AD} =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module