The cross product of the vectors 2i^-3j^+4k^ and i^+4j^-5k^ is

P¯=2i^-3j^+4k^, Q¯=i^+4j^-5k^P¯ x Q¯=i^j^k^2-3414-5=i^(+15-16)-j^(-10-4)+k^(8-(-3))=i^+14j^+11k^

The cross product of the vectors 2i^-3j^+4k^ and i^+4j^-5k^ is

P¯=2i^-3j^+4k^, Q¯=i^+4j^-5k^P¯ x Q¯=i^j^k^2-3414-5=i^(+15-16)-j^(-10-4)+k^(8-(-3))=i^+14j^+11k^

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The cross product of the vectors $(2 \hat{i} - 3 \hat{j} + 4 \hat{k})$ and $(\hat{i} + 4 \hat{j} - 5 \hat{k})$ is

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$- \hat{i} - 14 \hat{j} + 11 \hat{k}$

$\hat{i} + 14 \hat{j} + 11 \hat{k}$

$- \hat{i} + 14 \hat{j} + 11 \hat{k}$

$- \hat{i} + 14 \hat{j} + 5 \hat{k}$

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Detailed Solution

$\bar{P} = 2 \hat{i} - 3 \hat{j} + 4 \hat{k}, \bar{Q} = \hat{i} + 4 \hat{j} - 5 \hat{k}$

$\bar{P} x \bar{Q} = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & - 3 & 4 \\ 1 & 4 & - 5 \end{matrix}|$

$= \hat{i} (+ 15 - 16) - \hat{j} (- 10 - 4) + \hat{k} (8 - (- 3))$

$= \hat{i} + 14 \hat{j} + 11 \hat{k}$

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The cross product of the vectors 2i^-3j^+4k^ and i^+4j^-5k^ is

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The cross product of the vectors $(2 \hat{i} - 3 \hat{j} + 4 \hat{k})$ and $(\hat{i} + 4 \hat{j} - 5 \hat{k})$ is