Let a = 2 i - 5 j + 5 k and b = i - j + 3 k . If c is a vector such that 2 ( a × c ) + 3 ( b× c) = 0 and ( a - b ) · c = - 97 , then | c × k | 2 is equal to [2026]

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Solution

Q.
Let $\vec{a} = 2 \hat{i} - 5 \hat{j} + 5 \hat{k}$ and $\vec{b} = \hat{i} - \hat{j} + 3 \hat{k}$ . If $\vec{c}$ is a vector such that $2 (\vec{a} \times \vec{c}) + 3 (\vec{b} \times \vec{c}) = \vec{0}$ and $(\vec{a} - \vec{b}) \cdot \vec{c} = - 97,$ then $| \vec{c} \times \hat{k} |^{2}$ is equal to [2026]

1 218

2 205

3 193

4 233

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