Let a - i - j - k - b - i - j -2 k - and c - x i - x -2 j - k -If c - lies in the plane of a - and b -then x -A- NB- -2C- -1

The correct option is B 2Given a=î+ĵ+k̂, b=î ĵ+2k̂ and c=xî+(x 2)ĵ k̂ are coplanar. Since the three vectors are coplanar, their scalar triple product is 0. ⇒ 1 ...

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Byju's Answer

Standard XII

Mathematics

Test for Coplanarity

Let a →= i ∧∧...

Question

$L e t \to a = ˆ i + ˆ j + ˆ k, \to b = ˆ i - ˆ j + 2 ˆ k a n d \to c = x ˆ i + (x - 2) ˆ j - ˆ k . I f \to c l i e s i n t h e p l a n e o f \to a a n d \to b, t h e n x =$

0.0

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Solution

The correct option is B -2
Given $\to a =^i +^j +^k$ , $\to b =^i -^j + 2^k$ and $\to c = x^i + (x - 2)^j -^k$ are coplanar.
Since the three vectors are coplanar, their scalar triple product is 0.
$\Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 1 & - 1 & 2 x & x - 2 & - 1 \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} 1 & 0 & 0 1 & - 2 & 1 x & - 2 & - 1 - x \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow - 2 (- 1 - x) + 2 = 0 \Rightarrow x = - 2$

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Let →a=ˆi+ˆj+ˆk, →b=ˆi−ˆj+2 ˆk and→c=x ˆi+(x−2) ˆj−ˆk.If →c lies in the plane of →a and →b,then x=

$L e t \to a = ˆ i + ˆ j + ˆ k, \to b = ˆ i - ˆ j + 2 ˆ k a n d \to c = x ˆ i + (x - 2) ˆ j - ˆ k . I f \to c l i e s i n t h e p l a n e o f \to a a n d \to b, t h e n x =$