If the four points, whose position vectors are 3 hati-4 hatj+2 hatk, hati+2 hatj- hatk,-2 hati- hatj+3 hatk and 5 hat i -2 α hat j +4 hat k are coplanar, then α is equal to

Question

If the four points, whose position vectors are 3 hati-4 hatj+2 hatk, hati+2 hatj- hatk,-2 hati- hatj+3 hatk and 5 hat i -2 α hat j +4 hat k are coplanar, then α is equal to (A) (107/17) (B) (73/17) (C) -(73/17) (D) -(107/17)

Tardigrade Admin · Accepted Answer

Let A :(3,-4,2) C :(-2,-1,3) text B: (1,2,-1) text D: (5,-2 α, 4) A, B, C, D are coplanar points, then ⇒| 1-3 2+4 -1-2 -2-3 -1+4 3-2 5-3 -2 α+4 4-2|=0 ⇒ α=(73/17)

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

$\frac{107}{17}$

$\frac{73}{17}$

$- \frac{73}{17}$

$- \frac{107}{17}$

Let $A : (3, - 4, 2) C : (- 2, - 1, 3)$
$B : (1, 2, - 1) D : (5, - 2 α, 4)$
$A, B, C, D$ are coplanar points, then
$\Rightarrow ∣ ∣ 1 - 3 - 2 - 3 5 - 3 2 + 4 - 1 + 4 - 2 α + 4 - 1 - 2 3 - 2 4 - 2 ∣ ∣ = 0$
$\Rightarrow α = \frac{73}{17}$

Q. If the four points, whose position vectors are 3i^−4j^​+2k^,i^+2j^​−k^,−2i^−j^​+3k^ and 5i^−2αj^​+4k^ are coplanar, then α is equal to

17107​

1773​

−1773​

−17107​