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
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
$-1$
$0.5$
$-0.5$
$1$
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
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.
$\therefore \overrightarrow A \,.\,\overrightarrow B = - 8 + 12 + 8\alpha = 0$ $⇒$ $8\alpha = - 4$ $⇒$ $\alpha = - 1/2$
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