If \lambda_1 < \lambda_2 are two values of \lambda such that the angle between the planes P_1: \overline{ {\r}}(3 { {\i}}^{\^}-5 { {\j}}^{\^}+ { {\k}}^{\^})=7 and P_2: \overrightarrow{r} \cdot(\lambda\stackrel{\^}{i}+\stackrel{\^}{j}-3 \stackrel{\^}{k})=9 is \sin ^{-1} ( {2 \sqrt{6}}/{5}), then the square of the length of perpendicular from the point (38 \lambda_1, 10 \lambda_2, 2) to the plane P_1 is _______. [30-Jan-2023 Shift 1]

JEE Mains 30-Jan-2023 Shift 1 Solved Paper

Section: Mathematics

Question : 83 of 90

Marks: +1, -0

If λ1<λ2 are two values of λ such that the angle between the planes P1:r(3‌

−5‌

+‌

)=7 and P2:

→

⋅(λ

−3

)=9 is sin‌−1(‌

2√6

), then the square of the length of perpendicular from the point (38λ1,10λ2,2) to the plane P1 is _______.

[30-Jan-2023 Shift 1]

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