Question

$If \, \, \vec{a}=\hat{i}+2\hat{j}+3\hat{k}, \, \vec{b}= \, -\hat{i}+2\hat{j}+\hat{k}$ and $\vec{c} \, = \, 3\hat{i}+\hat{j}$ then t such that $\vec{a}+t\vec{b}$ is at right angle to $\vec{c}$ will be equal to

• A. 5
• B. 4
• C. 6
• D. 2

Answer 1

The Correct Option is A

We have, $\vec{a}+t\vec{b}=(\hat{i}+2\hat{j}+3\hat{k}) +t(-\hat{i}+2\hat{j}+\hat{k})$
$= \, (1-t)\hat{i} + (2+2t)\hat{j}+(3+t)\hat{k}$
It is $\bot$ to c= $3\hat{i} + \hat{j}$
If 3(1 - t) + (2 + 2t) + (3 + t) (0) = 0
$\Rightarrow $ 3 - 3t + 2 + 2t = 0 $\Rightarrow $ t = 5