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  • Let be the plane passing through the points (5, 3, 0), (13, 3, -2) and (1, 6, 2). For <img alt="\alpha \in N" src="https://en

Let P be the plane passing through the points (5, 3, 0), (13, 3, -2) and (1, 6, 2). For \alpha \in N,if the distances of the points \mathrm{A}(3,4, \alpha)\; and \; \mathrm{B}(2, \alpha,a) from the plane \mathrm{P}  are 2 and 3 respectively, then the positive value of a is

Option: 1

5


Option: 2

6


Option: 3

4


Option: 4

3


Answers (1)

best_answer

\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 8 & 0 & -2 \\ 4 & -3 & -2\end{array}\right|=\hat{i}(-6)+8 \hat{j}-24 \hat{k}

Normal of the plane =3 \hat{i}-4 \hat{j}+12 \hat{k}
Plane : 3 x-4 y+12 z=3

Distance from \mathrm{A}(3,4, \alpha)

\left|\frac{9-16+12 \alpha-3}{13}\right|=2
\alpha=3

\alpha=-8 (rejected)
\text{Distance from }B(2,3, a)
\left|\frac{6-12+12 a-3}{13}\right|=3
\mathrm{a}=4

 

Posted by

SANGALDEEP SINGH

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