Kinematics Question 603
Question: The vector having magnitude equal to 3 and perpendicular to the two vectors $ \vec{A}=2\hat{i}+2\hat{j}+\hat{k} $ and $ \vec{B}=2\hat{i}-2\hat{j}+3\hat{k} $ it’s:
Options:
A) $ \pm (2\hat{i}-\hat{j}-2\hat{k})~~~ $
B)$ \pm (3\hat{i}+\hat{j}-2\hat{k}) $
C) $ -(3\hat{i}+\hat{j}-3\hat{k})~ $
D)$ (3\hat{i}-\hat{j}-3\hat{k}) $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] The required vector is, $ =3\frac{(\vec{A}\times \vec{B})}{|\vec{A}\times \vec{B}|}=3\frac{[(2\hat{i}+2\hat{j}+\hat{k})\times (2\hat{i}-2\hat{j}+3\hat{k})]}{|\vec{A}\times \vec{B}|} $
$ =3\frac{(8\hat{i}-4\hat{j}-8\hat{k})}{\sqrt{8^{2}+4^{2}+8^{2}}}=2\hat{i}-\hat{j}-2\hat{k}. $
