Let p = 2i + j + 3k and q = i - j + k. If for some real numbers α, β, and γ, we have 15i + 10j + 6k = α (2p + q ) + β (p - 2q ) + γ (p × q ), then the value of γ is ______.

Let p = 2i + j + 3k and q = i - j + k. If for some real… — JEE Advanced 2024 Mathematics PYQ

JEE Advanced 2024 · Paper 2 · numerical answer

Let

\vec{p} = 2\hat{i} + \hat{j} + 3\hat{k}

and

\vec{q} = \hat{i} - \hat{j} + \hat{k}

. If for some real numbers

\alpha

\beta

, and

\gamma

, we have

15\hat{i} + 10\hat{j} + 6\hat{k} = \alpha\left(2\vec{p} + \vec{q}\right) + \beta\left(\vec{p} - 2\vec{q}\right) + \gamma\left(\vec{p} \times \vec{q}\right),

then the value of

\gamma

is ______.

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Answer: 2

[JEE Advanced 2024 · Paper 2]

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