Let a - i - j - k- b - i - j - 2k and c - xi - -x - 2-j - 1k are three vectors- If vector c lies in the plane of a and b- then x equals to- A- 0- B- 1- C- -4- D- -2- Maths Q-A

Explanation of correct option:Co planar vectors:When a,b,call lies on the same plane, this means they are co planar.So determinant formed by their coefficient i ...

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Byju's Answer

Standard XII

Mathematics

Test for Collinearity of Vectors

Let a = i + j...

Question

Let $\vec{a} = \hat{i} + \hat{j} + \hat{k}$ , $\vec{b} = \hat{i} - \hat{j} + 2 \hat{k}$ and $\vec{c} = x \hat{i} + (x - 2) \hat{j} - \hat{k}$ are three vectors. If vector $\vec{c}$ lies in the plane of $\vec{a}$ and $\vec{b}$ , then $x$ equals to:

$0$

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$1$

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$- 4$

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$- 2$

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Solution

The correct option is D
$- 2$

Explanation of correct option:
Co-planar vectors:
When $\vec{a}, \vec{b}, \vec{c}$ all lies on the same plane, this means they are co-planar.So determinant formed by their coefficient is zero.
Now,
$|\begin{matrix} x & x - 2 & - 1 \\ 1 & 1 & 1 \\ 1 & - 1 & 2 \end{matrix}| = 0 \Rightarrow 3 x + 2 - x + 2 = 0 \Rightarrow 2 x = - 4 \Rightarrow x = - 2$
Hence, the correct option is option (D).

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Let a→=i^+j^+k^ ,b→=i^-j^+2k^ and c→=xi^+(x-2)j^-k^ are three vectors. If vector c→ lies in the plane of a→ and b→, then x equals to:

The correct option is D -2Explanation of correct option:Co-planar vectors:When a→,b→,c→all lies on the same plane, this means they are co-planar.So determinant formed by their coefficient is zero.Now,xx-2-11111-12=0⇒3x+2-x+2=0⇒2x=-4⇒x=-2 Hence, the correct option is option (D).

Let $\vec{a} = \hat{i} + \hat{j} + \hat{k}$ , $\vec{b} = \hat{i} - \hat{j} + 2 \hat{k}$ and $\vec{c} = x \hat{i} + (x - 2) \hat{j} - \hat{k}$ are three vectors. If vector $\vec{c}$ lies in the plane of $\vec{a}$ and $\vec{b}$ , then $x$ equals to: