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If a vector 2\hat{i}+3\hat{j}+8\hat{k}is perpendicular to the vectors -4\hat{j}+4\hat{i}+\alpha \hat{k} Then the value of \alpha is

Option: 1

-1
 

 


Option: 2

\frac{1}{4 }


 


Option: 3

\frac{1}{2 }

 


Option: 4

-\frac{1}{2 }


Answers (1)

best_answer

      

 vectors are perpendicular so dot product should be zero

\\\left (2\hat{i}+3\hat{j}+8\hat{k} \right ).\left ( -4\hat{j}+4\hat{i}+\alpha \hat{k} \right )= 0\\\\\left (2\hat{i}+3\hat{j}+8\hat{k} \right ).\left ( 4\hat{i}-4\hat{j}+\alpha \hat{k} \right )= 0\\\\*8-12+8\alpha = 0 \\\\*\alpha = \frac{1}{2} 

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