Kinematics Question 252
Question: If a vector $ 2\hat{i}+3\hat{j}+8\hat{k} $ is perpendicular to the vector $ 4\hat{j}-4\hat{i}+\alpha \hat{k} $ . Then the value of $ \alpha $ it’s [CBSE PMT 2005]
Options:
A) ?1
B) $ \frac{1}{2} $
C) $ -\frac{1}{2} $
D) 1
Correct Answer: C Given vectors can be rewritten as $ \overrightarrow{A}=2\hat{i}+3\hat{j}+8\hat{k} $ and $ \overrightarrow{B}=-4\hat{i}+4\hat{j}+\alpha \hat{k} $ Dot product of these vectors should be equal to zero because they are perpendicular. $ \overrightarrow{A}.\overrightarrow{B}=-8+12+8\alpha =0 $ therefore $ 8\alpha =-4 $ therefore $ \alpha =-1/2 $
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