Let a - 2 - - 3 - - k- b - - - - 2 - - 4k-c - - - - - k- d - - - - - k- then a-b-c-d is equal to

Scalar product of four vectors(a×b).(c×d) ⇒a.c amp; a.d b.c amp; b.d ⇒( 2 î + 3 ĵ k̂).( î + ĵ + k̂) amp; (2 î + 3 ĵ k̂).( î ĵ k̂) ( î + 2 ĵ 4k ...

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Standard XII

Mathematics

Dot Product of Two Vectors

Let a = 2 î +...

Question

Let $\to a = 2^i + 3^j -^k, \to b = -^i + 2^j - 4^k, \to c =^i +^j +^k, \to d =^i -^j -^k,$ then $(\to a \times \to b) . (\to c \times \to d)$ is equal to

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Solution

The correct option is D $4$
Scalar product of four vectors $(\to a \times \to b) . (\to c \times \to d)$
$\Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} \to a . \to c & \to a . \to d \to b . \to c & \to b . \to d \end{matrix} ∣ ∣ ∣ ∣$
$\Rightarrow ∣ ∣ ∣ \begin{matrix} (2^i + 3^j -^k) . (^i +^j +^k) & (2^i + 3^j -^k) . (^i -^j -^k) (-^i + 2^j - 4^k) . (^i +^j +^k) & (-^i + 2^j - 4^k) . (^i -^j -^k) \end{matrix} ∣ ∣ ∣$
$\Rightarrow ∣ ∣ ∣ \begin{matrix} (2 + 3 - 1) & (2 - 3 + 1) (- 1 + 2 - 4) & (- 1 - 2 + 4) \end{matrix} ∣ ∣ ∣$
$\Rightarrow ∣ ∣ ∣ \begin{matrix} 4 & 0 - 3 & 1 \end{matrix} ∣ ∣ ∣ = 4 - 0 = 4$

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Dot Product of Two Vectors

Standard XII Mathematics

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Let →a=2^i+3^j−^k,→b=−^i+2^j−4^k,→c=^i+^j+^k, →d=^i−^j−^k, then (→a×→b).(→c×→d) is equal to

Let $\to a = 2^i + 3^j -^k, \to b = -^i + 2^j - 4^k, \to c =^i +^j +^k, \to d =^i -^j -^k,$ then $(\to a \times \to b) . (\to c \times \to d)$ is equal to