The value of k for which the vectors vec{a} = | vedclass

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

Question

(A) Two vectors $\vec{a}$ and $\vec{b}$ are collinear if $\vec{a} = m\vec{b}$ for some non-zero scalar $m$.Given $\vec{a} = \hat{i} - \hat{j}$ and $\v

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) Two vectors $\vec{a}$ and $\vec{b}$ are collinear if $\vec{a} = m\vec{b}$ for some non-zero scalar $m$.Given $\vec{a} = \hat{i} - \hat{j}$ and $\vec{b} = -2\hat{i} + k\hat{j}$.Substituting the vectors,we get $\hat{i} - \hat{j} = m(-2\hat{i} + k\hat{j})$.Equating the coefficients of $\hat{i}$ and $\hat{j}$ on both sides:For $\hat{i}$: $1 = -2m \implies m = -1/2$.For $\hat{j}$: $-1 = mk$.Substituting $m = -1/2$ into the second equation: $-1 = (-1/2)k$.Solving for $k$,we get $k = 2$.

The value of $k$ for which the vectors $\vec{a} = \hat{i} - \hat{j}$ and $\vec{b} = -2\hat{i} + k\hat{j}$ are collinear is

Similar Questions

If $p = 7i - 2j + 3k$ and $q = 3i + j + 5k$,then $|p - 2q| = \dots$

If $ABCDEFGH$ is a convex octagon,then $\vec{AB} + \vec{BC} + \vec{CD} + \vec{DE} + \vec{AH} + \vec{HG} + \vec{GF} + \vec{FE} = $

If $\bar{c} = 5\bar{a} + 6\bar{b}$ and $3\bar{c} = \bar{a} - 4\bar{b}$,then:

If the sides of a regular hexagon $ABCDEF$ are given by $\vec{AB} = \bar{a}$ and $\vec{BC} = \bar{b}$,then $\vec{FA} = .....$

The position vector of a point at a distance of $3\sqrt{11}$ units from $i - j + 2k$ on a line passing through the points $i - j + 2k$ and $3i + j + k$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module