If a vector 2hat{i} + 3hat{j} + 8hat{k} is perpendicular to vector 4hat{j} - 4hat{i} + α hat{k} . T

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3-1.Vectors

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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 $ is

A

$-1$

B

$0.5$

C

$-0.5$

D

$1$

(AIPMT-2005)

Solution

(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.

$\therefore \overrightarrow A \,.\,\overrightarrow B = – 8 + 12 + 8\alpha = 0$ $⇒$ $8\alpha = – 4$ $⇒$ $\alpha = – 1/2$

Standard 11

Physics

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