If a and b are two vectors- such that a- b - 0 and -a-b- - -a-b- then angle between vector a and b is

The correct option is A 3π4 Given, |a.b| = |a × b| |a||b||cosθ| = |a||b| |sinθ| (where θ is angle between a and b ) ⇒ |cosθ ...

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Byju's Answer

Standard XII

Mathematics

Angle between Two Vectors

If a and ...

Question

If $¯ ¯ ¯ a$ and $¯ ¯ b$ are two vectors, such that $¯ ¯ ¯ a . ¯ ¯ b < 0$ and $| ¯ ¯ ¯ a . ¯ ¯ b | = | ¯ ¯ ¯ a \times ¯ ¯ b |$ , then angle between vector $¯ ¯ ¯ a$ and $¯ ¯ b$ is

π

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\frac{4 π}{4}

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\frac{π}{4}

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\frac{3 π}{4}

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Solution

The correct option is A $\frac{3 π}{4}$
Given, $| a . b | = | a \times b |$
$| ¯ ¯ ¯ a | | ¯ ¯ b | | cos θ | = | ¯ ¯ ¯ a | | ¯ ¯ b | | sin θ |$
(where $θ$ is angle between $¯ ¯ ¯ a$ and $¯ ¯ b$ )
$\Rightarrow | cos θ | = | sin θ |$
$θ = \frac{π}{4}$ or $\frac{3 π}{4}$ (as $0 \leq θ \leq π$ )
But $¯ ¯ ¯ a . ¯ ¯ b < 0$
$∴ θ = \frac{3 π}{4}$

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If ¯¯¯a and ¯¯b are two vectors, such that ¯¯¯a.¯¯b<0 and |¯¯¯a.¯¯b|=|¯¯¯a×¯¯b|, then angle between vector ¯¯¯a and ¯¯b is

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If $¯ ¯ ¯ a$ and $¯ ¯ b$ are two vectors, such that $¯ ¯ ¯ a . ¯ ¯ b < 0$ and $| ¯ ¯ ¯ a . ¯ ¯ b | = | ¯ ¯ ¯ a \times ¯ ¯ b |$ , then angle between vector $¯ ¯ ¯ a$ and $¯ ¯ b$ is