The value of α for which point M(α hati+2 hatj+ hatk), lies in the plane containing three points A( hati+ hatj+ hatk), B (2 hat i +2 hat j + hat k ) and C (3 hat i - hat k ) is

Question

The value of α for which point M(α hati+2 hatj+ hatk), lies in the plane containing three points A( hati+ hatj+ hatk), B (2 hat i +2 hat j + hat k ) and C (3 hat i - hat k ) is (A) 1 (B) 2 (C) (1/2) (D) (-1/2)

Tardigrade Admin · Accepted Answer

The equation of plane containing A , B and C is |x -1 y -1 z -1 1 1 0 2 -1 -2|=0 ⇒ -2 x +2 y -3 z +3=0....(1) text Clearly, M (α, 2,1) text satisfy equation (1) text , so -2 α+4-3+3=0 ⇒ α=2

Q. The value of $α$ for which point $M (α \hat{i} + 2 \hat{j} + \hat{k})$ , lies in the plane containing three points $A (\hat{i} + \hat{j} + \hat{k})$ , $B (2 \hat{i} + 2 \hat{j} + \hat{k})$ and $C (3 \hat{i} - \hat{k})$ is

1

2

$\frac{1}{2}$

$\frac{- 1}{2}$

The equation of plane containing $A, B$ and $C$ is
$∣ ∣ x - 1 12 y - 1 1 - 1 z - 1 0 - 2 ∣ ∣ = 0$
$\Rightarrow - 2 x + 2 y - 3 z + 3 = 0$ ....(1)
$Clearly, M (α, 2, 1) satisfy equation (1), so$
$- 2 α + 4 - 3 + 3 = 0 \Rightarrow α = 2$

Q. The value of α for which point M(αi^+2j^​+k^), lies in the plane containing three points A(i^+j^​+k^), B(2i^+2j^​+k^) and C(3i^−k^) is

1

2

21​

2−1​

The equation of plane containing A,B and C is ∣∣​x−112​y−11−1​z−10−2​∣∣​=0 ⇒−2x+2y−3z+3=0....(1) Clearly, M(α,2,1) satisfy equation (1), so −2α+4−3+3=0⇒α=2

Q. The value of $α$ for which point $M (α \hat{i} + 2 \hat{j} + \hat{k})$ , lies in the plane containing three points $A (\hat{i} + \hat{j} + \hat{k})$ , $B (2 \hat{i} + 2 \hat{j} + \hat{k})$ and $C (3 \hat{i} - \hat{k})$ is

$\frac{1}{2}$

$\frac{- 1}{2}$

The equation of plane containing $A, B$ and $C$ is
$∣ ∣ x - 1 12 y - 1 1 - 1 z - 1 0 - 2 ∣ ∣ = 0$
$\Rightarrow - 2 x + 2 y - 3 z + 3 = 0$ ....(1)
$Clearly, M (α, 2, 1) satisfy equation (1), so$
$- 2 α + 4 - 3 + 3 = 0 \Rightarrow α = 2$