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

Show Answer

Answer:

Correct Answer: C

Solution:

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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