If - 3 a- -b- -a-b- the angle between vector a- and vector b- is-

The correct option is A π/3 √(3) a⃗·b⃗ = | a × b | ( Given) As we know that angle between the two vectors is given as sinθ = | a × b || a | | ...

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Byju's Answer

Standard XII

Mathematics

Applications of Cross Product

If √ 3 a̅ ....

Question

If $\sqrt{3} ¯ a . ¯ b = | ¯ a \times ¯ b |$ the angle between vector $¯ a$ and vector $¯ b$ is:

\frac{π}{2}

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\frac{π}{6}

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\frac{π}{4}

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\frac{π}{3}

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Solution

The correct option is A $\frac{π}{3}$
$\sqrt{3} \to a \cdot \to b = | a \times b | (Given)$
As we know that angle between the two vectors is given as-
$sin θ = \frac{| a \times b |}{| a | | b |}$
$\Rightarrow sin θ = \frac{\sqrt{3} \to a \cdot \to b}{| a | | b |}$
$\Rightarrow \frac{sin θ}{\sqrt{3}} = \frac{\to a \cdot \to b}{| a | | b |} . . . . . (1)$
$cos θ = \frac{\to a \cdot \to b}{| a | | b |} . . . . . (2)$
From equation $(1)$ and $(2)$ , we have
$\frac{sin θ}{\sqrt{3}} = cos θ$
$\frac{sin θ}{cos θ} = \sqrt{3}$
$tan θ = tan \frac{π}{3}$
$\Rightarrow θ = \frac{π}{3}$

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If √3¯a.¯b=|¯a×¯b| the angle between vector ¯a and vector ¯b is:

If $\sqrt{3} ¯ a . ¯ b = | ¯ a \times ¯ b |$ the angle between vector $¯ a$ and vector $¯ b$ is: