Let a-b-k- -b- If the vectors- -2-k- 3-2-k- - are coplanor then - is

The correct option is B 3 The vectors î 2ĵ+k̂, #160;3î+2ĵ k̂ amp; #160; α(î + ĵ) + β(ĵ + k̂) are coplanar. ⇒ 1 amp; 2 amp; ...

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Byju's Answer

Standard XII

Mathematics

Cross Product of Two Vectors

Let a̅=î+ĵ,...

Question

Let $¯ a =^i +^j,^b =^j +^k$ & $^c = α^a + β^b$ . If the vectors, $^i - 2^j +^k$ , $3^i + 2^j -^k$ & $^c$ are coplanor then $\frac{α}{β}$ is

1

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- 3

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Solution

The correct option is B $- 3$
The vectors $^i - 2^j +^k, 3^i + 2^j -^k$ & $α (^i +^j) + β (^j +^k)$ are coplanar.

$\Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} 1 & - 2 & 1 3 & 2 & - 1 α & α + β & β \end{matrix} ∣ ∣ ∣ ∣ = 0$
$\Rightarrow 1 (α + 3 β) + 2 (3 β + α) + 1 (α + 3 β) = 0$
$\Rightarrow 4 α + 12 β = 0$
$\Rightarrow \frac{α}{β} = - 3$

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Let ¯a=^i+^j,^b=^j+^k & ^c=α^a+β^b. If the vectors, ^i−2^j+^k, 3^i+2^j−^k & ^c are coplanor then αβ is

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