If the four points with position vectors -2 hati+ hatj+k, hati + hatj+ hatk, hatj- hatk, and λ hatj+ hatk are coplanar, then λ=

Question

If the four points with position vectors -2 hati+ hatj+k, hati + hatj+ hatk, hatj- hatk, and λ hatj+ hatk are coplanar, then λ= (A) 1 (B) 2 (C) -1 (D) 0

Tardigrade Admin · Accepted Answer

If four points (x1, y1, z1),(x2, y2, z2),(x3, y3, z3) and (x4, y4, z4) are coplanar, then |x2-x1 y2-y1 z2-z1 x3-x1 y3-y1 z3-z1 x4-x1 y4-y1 z4-z1|=0 Now, |3 0 0 2 0 -2 2 λ-1 0|=0 ⇒ 3(0+2 λ-2)=0 ⇒ λ=1

Q. If the four points with position vectors −2i^+j^​+k,i^+j^​+k^,j^​−k^, and λj^​+k^ are coplanar, then λ=

1

2

-1

0

Q. If the four points with position vectors $- 2 \hat{i} + \hat{j} + k, \hat{i} + \hat{j} + \hat{k}, \hat{j} - \hat{k},$ and $λ \hat{j} + \hat{k}$ are coplanar, then $λ =$