If the four pointegrals, whose position vectors are (3 \hat{... | Mathematics | SolveeIt | Solveeit

Today, August 18

Question

If the four points, whose position vectors are $3 \hat{i}-4 j+2 \hat{k}, l+2 j-\hat{k}_4-2 \hat{k}-j+3 \hat{k}$ and $5 \hat{i}-2 \alpha \hat{j}+4 \hat{k}$ are coplanar, then a is equal to

A

$\frac{107}{17}$

B

$\frac{73}{17}$

C

$-\frac{73}{17}$

D

$-\frac{107}{17}$

Answer

$\frac{73}{17}$

Explanation

Solution

The correct answer is (B) : $\frac{73}{17}$
Let A:(3,−4,2)C:(−2,−1,3)
B : (1,2,−1) D : (5,−2α,4)
A,B,C,D are coplanar points, then
⇒∣∣1−3−2−35−32+4−1+4−2α+4−1−23−24−2∣∣=0
⇒α=1773