The number of values of m in R for which the | vedclass

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

Question

(C) Two vectors $\vec{a} = a_1 \hat{i} + b_1 \hat{j} + c_1 \hat{k}$ and $\vec{b} = a_2 \hat{i} + b_2 \hat{j} + c_2 \hat{k}$ are collinear if their com

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(C) Two vectors $\vec{a} = a_1 \hat{i} + b_1 \hat{j} + c_1 \hat{k}$ and $\vec{b} = a_2 \hat{i} + b_2 \hat{j} + c_2 \hat{k}$ are collinear if their components are proportional,i.e.,$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} = k$ for some constant $k$.Given vectors are $\vec{a} = \hat{i} + 2 \hat{j} + m \hat{k}$ and $\vec{b} = \hat{i} + m \hat{j} + 2 \hat{k}$.For these to be collinear,we must have $\frac{1}{1} = \frac{2}{m} = \frac{m}{2}$.From $\frac{1}{1} = \frac{2}{m}$,we get $m = 2$.From $\frac{1}{1} = \frac{m}{2}$,we get $m = 2$.Since both conditions yield the same value $m = 2$,there is only $1$ such value of $m$ for which the vectors are collinear.

The number of values of $m \in R$ for which the vectors $\hat{i}+2 \hat{j}+m \hat{k}$ and $\hat{i}+m \hat{j}+2 \hat{k}$ are collinear is

Similar Questions

The position vectors of four points $P, Q, R, S$ are $2a + 4c$,$5a + 3\sqrt{3}b + 4c$,$-2\sqrt{3}b + c$,and $2a + c$ respectively. Then:

Find the position vector of the point on the line passing through the point $\hat{i} - \hat{j} + 2\hat{k}$ and parallel to the vector $3\hat{i} + \hat{j} + \hat{k}$,which is at a distance of $3\sqrt{11}$ units from the point $\hat{i} - \hat{j} + 2\hat{k}$.

Find the position vector of the midpoint of the vector joining the points $P(2, 3, 4)$ and $Q(4, 1, -2)$.

If $a$ and $b$ are the position vectors of $A$ and $B$ respectively,then the position vector of a point $C$ on $AB$ produced such that $\overrightarrow{AC} = 3\overrightarrow{AB}$ is

Classify the following measure as a scalar or a vector:
$2 \text{ meters north-west}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module