Let `vec a ` be vector parallel to line of intersection of planes `P_1 and P_2` through origin. If `P_1`is parallel to the vectors `2 bar j + 3 bar k and 4 bar j - 3 bar k` and `P_2` is parallel to `bar j - bar k` and ` 3 bar I + 3 bar j `, then the angle between `vec a` and `2 bar i +bar j - 2 bar k` is :A. `(pi)/(2)`B. `(pi)/(4)`C. `(pi)/(6)`D. `(3pi)/(4)`

Let `vec a ` be vector parallel to line of intersection of planes `P_1

1.	Let `vec a ` be vector parallel to line of intersection of planes `P_1 and P_2` through origin. If `P_1`is parallel to the vectors `2 bar j + 3 bar k and 4 bar j - 3 bar k` and `P_2` is parallel to `bar j - bar k` and ` 3 bar I + 3 bar j `, then the angle between `vec a` and `2 bar i +bar j - 2 bar k` is :A. `(pi)/(2)`B. `(pi)/(4)`C. `(pi)/(6)`D. `(3pi)/(4)`
Answer» Correct Answer - B::D Let vector `vec(AO) ` be parallel to line of intersection of planes `P_(1) " and " P_(2) ` through origin . Normal to plane `P_(1)` is ` vec(n)_(1) =[(2hat(j) + 3hat(k)) xx (4hat(j) - 3hat(k))] =- 18hat(j)` So , `vec(OA) ` is parallel to `+- (vec(n)_(1) xx vec(n)_(2)) = 54 hat(j) - 54 hat(k)` `:. ` Angle between `54 (hat(j) - hat(k)) " and " (2hat(i) + hat(j) - 2hat(k)) ` is `" cos" 0 = +- ((54 + 108)/(3.54 "."sqrt(2))) =+- (1)/(sqrt(2))` ` :. 0 = (pi)/( 4) , ( 3pi)/(4)` Hence (b) and (d) are correct answers

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