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}. $



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