Let be a non-zero vector parallel to the line of intersection of the two planes described by and . If is the angle between the vector and the vector and , then the ordered pair is equal to:

Explanation: The given vectors describing the planes are and . Normal vectors of the planes First plane normal: Second plane normal: Direction vector of line of intersection So we take . Given and (satisfied). Angle between a⃗\vec a a and b⃗\vec b b \Rightarrow Magnitude of cross product Final Answer

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Let $a$ be a non-zero vector parallel to the line of intersection of the two planes described by $\hat{i} + \hat{j}, \hat{i} + \hat{k}$ and $\hat{i} - \hat{j}, \hat{i} - \hat{k}$ . If $θ$ is the angle between the vector $a$ and the vector $b = 2 \hat{i} - 2 \hat{j} + \hat{k}$ and $a \cdot b = 6$ , then the ordered pair $(θ, ∣ a \times b ∣)$ is equal to:

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