If the vectors 2 - - - - k- - - - 2 - - 3 k- and 3 - - - - 5 k- be coplanar- then - -

The correct option is D 4 [ | [ 2 amp; 1 amp; 1; 1 amp; 2 amp; 3; 3 amp; λ #160; amp; 5 ]| =0; ...

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Byju's Answer

Standard XII

Mathematics

Test for Coplanarity

If the vector...

Question

If the vectors $2^i -^j +^k,^i + 2^j - 3^k$ and $3^i + λ^j + 5^k$ be coplanar, then $λ =$

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Solution

The correct option is D $- 4$
$\begin{matrix} ∣ ∣ ∣ ∣ \begin{matrix} 2 & - 1 & 1 1 & 2 & - 3 3 & λ & 5 \end{matrix} ∣ ∣ ∣ ∣ = 0 = 2 (10 + 3 λ) + (5 + 9) + (λ - 6) = 20 + 6 λ + λ + 8 = 0 = 7 λ + 28 = 0 λ = - 4 H e n c e, o p t i o n D i s c o r r e c t a n s w e r . \end{matrix}$

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If the vectors 2^i−^j+^k,^i+2^j−3^k and 3^i+λ^j+5^k be coplanar, then λ=

The correct option is D −4∣∣ ∣∣2−1112−33λ5∣∣ ∣∣=0=2(10+3λ)+(5+9)+(λ−6)=20+6λ+λ+8=0=7λ+28=0λ=−4Hence,optionDiscorrectanswer.

If the vectors $2^i -^j +^k,^i + 2^j - 3^k$ and $3^i + λ^j + 5^k$ be coplanar, then $λ =$