Let A¯ be vector parallel to line of intersection of planes P1 and P2 through origin. P1 is parallel to the vectors 2j^+3k^ and 4j^−3k^ and P2 is parallel to j^−k^ and 3i^+3j^, then the acute angle between the lines having their directions along A¯ and 2i^+j^−2k^ is 2πn, where n=___

Normal of P1 will be along i^ and Normal of P2 will be along i^−j^−k^So, line of intersection will be along j^−k^So, acute angle between j^−k^ and 2i^+j^−2k^ will be π4

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Let $\bar{A}$ be vector parallel to line of intersection of planes $P_{1}$ and $P_{2}$ through origin. $P_{1}$ is parallel to the vectors $2 \hat{j} + 3 \hat{k}$ and $4 \hat{j} - 3 \hat{k}$ and $P_{2}$ is parallel to $\hat{j} - \hat{k}$ and $3 \hat{i} + 3 \hat{j},$ then the acute angle between the lines having their directions along $\bar{A}$ and $2 \hat{i} + \hat{j} - 2 \hat{k}$ is $\frac{2 π}{n},$ where $n =___$

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Detailed Solution

Normal of $P_{1}$ will be along $\hat{i}$ and Normal of $P_{2}$ will be along $\hat{i} - \hat{j} - \hat{k}$
So, line of intersection will be along $\hat{j} - \hat{k}$
So, acute angle between $\hat{j} - \hat{k}$ and $2 \hat{i} + \hat{j} - 2 \hat{k}$ will be $\frac{π}{4}$