Angle between the vectors 3- -2- -k- and 2- - -4k- is

The correct option is C π 2 Let the two vectors be a and b respectively [ a⃗ =3î 2ĵ+k̂ ...

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Standard XII

Mathematics

Angle between Two Lines

Angle between...

Question

Angle between the vectors $3^i - 2^j +^k a n d 2^i +^j - 4^k$ is

\frac{π}{6}

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\frac{π}{3}

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\frac{π}{2}

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\frac{π}{4}

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Solution

The correct option is C $\frac{π}{2}$
Let the two vectors be a and b respectively
$\begin{matrix} \to a = 3^i - 2^j +^k \to b = 2^i +^j - 4^k \to a \cdot \to b = | \to a | ∣ ∣ \to b ∣ ∣ cos θ \to a \cdot \to b = 6 - 2 - 4 \to a \cdot \to b = 0 | \to a | = \sqrt{14} ∣ ∣ \to b ∣ ∣ = \sqrt{21} 0 = \sqrt{14} \sqrt{21} cos θ 0 = cos θ θ = 90^{0} = \frac{π}{2} \end{matrix}$

Hence, this is the answer.

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