If a - - -k- - b -2- - -k- - c - - -4k- and a - b - c -10- then - is equal to

The correct option is A 6 a. (b×c) = 10 #160; #160; #160; #160; #160;....Given ∴ 1 amp; 1 amp; 1 2 amp; λ amp; 1 ...

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Byju's Answer

Standard XII

Mathematics

Condition for Two Lines to be on the Same Plane

If a =î +ĵ ...

Question

If $¯ ¯ ¯ a =^i +^j +^k, ¯ ¯ b = 2^i + λ^j +^k, ¯ ¯ c =^i -^j + 4^k$ and $¯ ¯ ¯ a . (¯ ¯ b \times ¯ ¯ c) = 10$ , then $λ$ is equal to

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Solution

The correct option is A $6$
$¯ ¯ ¯ a . (¯ ¯ b \times ¯ ¯ c) = 10$ ....Given

$∴ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 2 & λ & 1 1 & - 1 & 4 \end{matrix} ∣ ∣ ∣ ∣ = 10$

$1 (4 λ + 1) - 1 (8 - 1) + 1 (- 2 - λ) = 10$
$3 λ = 18$
$λ = 6$
Hence, option A is correct.

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Similar questions

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If ¯¯¯a=^i+^j+^k,¯¯b=2^i+λ^j+^k,¯¯c=^i−^j+4^k and ¯¯¯a.(¯¯b×¯¯c)=10, then λ is equal to

The correct option is A 6¯¯¯a.(¯¯b×¯¯c)=10 ....Given∴∣∣ ∣∣1112λ11−14∣∣ ∣∣=101(4λ+1)−1(8−1)+1(−2−λ)=103λ=18λ=6Hence, option A is correct.

If $¯ ¯ ¯ a =^i +^j +^k, ¯ ¯ b = 2^i + λ^j +^k, ¯ ¯ c =^i -^j + 4^k$ and $¯ ¯ ¯ a . (¯ ¯ b \times ¯ ¯ c) = 10$ , then $λ$ is equal to

The correct option is A $6$
$¯ ¯ ¯ a . (¯ ¯ b \times ¯ ¯ c) = 10$ ....Given

$∴ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 2 & λ & 1 1 & - 1 & 4 \end{matrix} ∣ ∣ ∣ ∣ = 10$

$1 (4 λ + 1) - 1 (8 - 1) + 1 (- 2 - λ) = 10$
$3 λ = 18$
$λ = 6$
Hence, option A is correct.