The sum of all values of , for which the points whose position vectors are , , and are coplanar, is equal to:

2 Explanation: Are coplanar if Sum of all values of

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

The sum of all values of $α$ , for which the points whose position vectors are $\hat{i} - 2 \hat{j} + 3 \hat{k}$ , $2 \hat{i} - 3 \hat{j} + 4 \hat{k}$ , $(α + 1) \hat{i} + 2 \hat{k}$ and $9 \hat{i} + (α - 8) \hat{j} + 6 \hat{k}$ are coplanar, is equal to:

Choose the correct answer:

A.
-2
B.
2
(Correct Answer)
C.
6
D.
4

Correct Answer:

Explanation

$A B = O B - O A$

$A C = O C - O A$

Are coplanar if $[A B A C A D] = 0$

$\Rightarrow 1 α 8 am p; - 1 am p; 2 am p; α - 6 am p; 1 am p; - 1 am p; 3 = 0$

$\Rightarrow α = 4, - 2$
Sum of all values of $α = 2$

Explanation

$A B = O B - O A$

$A C = O C - O A$

Are coplanar if $[A B A C A D] = 0$

$\Rightarrow 1 α 8 am p; - 1 am p; 2 am p; α - 6 am p; 1 am p; - 1 am p; 3 = 0$

$\Rightarrow α = 4, - 2$
Sum of all values of $α = 2$

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