Question

If a vector 2i^ +3j^+8k^ is perpendicular to the vector 4j^_4i^+xk^ then find the value of x

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Answer 1

Answer:

$\boxed{\mathfrak{x = - \dfrac{1}{2}}}$

Given:

$\rm \overrightarrow{A} = 2 \hat{i} + 3 \hat{j} + 8 \hat{k} \\ \\ \rm \overrightarrow{B} = - 4 \hat{i} + 4 \hat{j} + x \hat{k} \\ \\ \rm A \perp B$

Explanation:

Dot product of two perpendicular vector is equal to zero.

$\rm \implies \overrightarrow{A}.\overrightarrow{B} = 0 \\ \\ \rm \implies (2 \hat{i} + 3 \hat{j} + 8 \hat{k}). (- 4 \hat{i} + 4 \hat{j} + x \hat{k}) = 0 \\ \\ \rm \implies - 8 + 12 + 8x = 0 \\ \\ \rm \implies 4 + 8x = 0 \\ \\ \rm \implies 8x = - 4 \\ \\ \rm \implies x = - \frac{4}{8} \\ \\ \rm \implies x = - \frac{1}{2}$

Answer 2

Answer:

(2i + 3j + 8k).(4j - 4i + xk) = 0

-8 + 12 + 8x = 0

x = -4/8

x = -1/2

x = -0.5