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

The sum of two forces is $18 \ N$ and the resultant,whose direction is at right angles to the smaller force,is $12 \ N$. The magnitudes of the two forces are:

The magnitude of the sum of vectors $(1, -\sqrt{2})$ and $(2, \sqrt{2})$ is $\ldots$

$A$ unit vector which is in the opposite direction of $(2, -2, 1)$ is $........$

If three points $A$,$B$,and $C$ have position vectors $(1, x, 3)$,$(3, 4, 7)$,and $(y, -2, -5)$ respectively and if they are collinear,then $(x, y)$ is

In the given figure (a square),identify the co-initial vectors.

Vedclass Test Series

Exam Paper Generator

Online Exam Module