If two vectors A - and B - are such that A - B - A - B - then the angle between A - and B - isA- 900B- Less than 900C- More than 900

The correct option is B Less than nbsp;90οWe know that, A→+B→=A2+B2+2ABcosθSimilary, nbsp;A→ B→=A2+( B)2+2A( B)cosθ∵A→+B→ nbsp; gt; nbsp;A→ B→⇒A→+B→2 ...

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Byju's Answer

Standard X

Mathematics

Addition of Vectors

If two vector...

Question

$If two vectors \to A and \to B are such that (\to A + \to B ∣ ∣ ∣ > (\to A - \to B ∣ ∣ ∣ then the angle between \to A and \to B is$

90^{ο}

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Less than

90^{ο}

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More than

90^{ο}

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Solution

The correct option is B Less than $90^{ο}$
We know that,
$(\to A + \to B ∣ ∣ ∣ = \sqrt{A^{2} + B^{2} + 2 ABcosθ} S imilary, (\to A - \to B ∣ ∣ ∣ = \sqrt{A^{2} + {(- B)}^{2} + 2 A (- B) cosθ} ∵ (\to A + \to B ∣ ∣ ∣ > (\to A - \to B ∣ ∣ ∣ \Rightarrow {(\to A + \to B ∣ ∣ ∣}^{2} > {(\to A - \to B ∣ ∣ ∣}^{2} \Rightarrow A^{2} + B^{2} + 2 AB cos θ > A^{2} + B^{2} - 2 AB c os θ O n solving we get cos θ > 0 ∴ θ < 90 °$

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If two vectors →A and →B are such that (→A+→B∣∣∣ > (→A−→B∣∣∣ then the angle between →A and →B is

$If two vectors \to A and \to B are such that (\to A + \to B ∣ ∣ ∣ > (\to A - \to B ∣ ∣ ∣ then the angle between \to A and \to B is$