If the points P, Q and R have the position ve | vedclass

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

Question

(A) Let the position vectors of points $P, Q$ and $R$ be $\vec{p} = \hat{i}-2 \hat{j}+3 \hat{k}$,$\vec{q} = -2 \hat{i}+3 \hat{j}+2 \hat{k}$ and $\vec{

Vedclass · Accepted Answer

collinear and $Q$ lies between $P$ and $R$.

Vedclass · Answer

(A) Let the position vectors of points $P, Q$ and $R$ be $\vec{p} = \hat{i}-2 \hat{j}+3 \hat{k}$,$\vec{q} = -2 \hat{i}+3 \hat{j}+2 \hat{k}$ and $\vec{r} = -8 \hat{i}+13 \hat{j}$.First,we find the vectors $\vec{PQ}$ and $\vec{QR}$:$\vec{PQ} = \vec{q} - \vec{p} = (-2 \hat{i}+3 \hat{j}+2 \hat{k}) - (\hat{i}-2 \hat{j}+3 \hat{k}) = -3 \hat{i}+5 \hat{j}-\hat{k}$.$\vec{QR} = \vec{r} - \vec{q} = (-8 \hat{i}+13 \hat{j}) - (-2 \hat{i}+3 \hat{j}+2 \hat{k}) = -6 \hat{i}+10 \hat{j}-2 \hat{k}$.We observe that $\vec{QR} = 2(-3 \hat{i}+5 \hat{j}-\hat{k}) = 2 \vec{PQ}$.Since $\vec{QR}$ is a scalar multiple of $\vec{PQ}$,the vectors $\vec{PQ}$ and $\vec{QR}$ are parallel.Because they share a common point $Q$,the points $P, Q$ and $R$ are collinear.Since $\vec{QR} = 2 \vec{PQ}$,the point $Q$ lies between $P$ and $R$.

If the points $P, Q$ and $R$ have the position vectors $\hat{i}-2 \hat{j}+3 \hat{k}$,$-2 \hat{i}+3 \hat{j}+2 \hat{k}$ and $-8 \hat{i}+13 \hat{j}$ respectively,then these points are

Similar Questions

The sum of the lengths of projections of $p \hat{i} + q \hat{j} + r \hat{k}$ on the coordinate axes, where $p = 4, q = -5, r = 7$, is: (in $\text{ units}$)

If $G$ is the centroid of the $\triangle ABC$,then $\vec{GA} + \vec{GB} + \vec{GC}$ is equal to

$A$ vector $\bar{a}$ has components $1$ and $2p$ with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counter-clockwise sense. If,with respect to the new system,$\bar{a}$ has components $1$ and $(p+1)$,then:

If the position vectors of the vertices of a triangle are $6i + 4j + 5k$,$4i + 5j + 6k$,and $5i + 6j + 4k$,then the triangle is

The system of unit vectors $i, j, k$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module