If - and - are two vectors such that - - - - - - - - then - and - are inclined at

The correct option is B An obtuse angleGiven relation #160; | α⃗+β⃗ | lt; | α⃗ β⃗ | On squaring both sides ( | α⃗+β⃗ |)^2 lt;( | α⃗ β⃗ |)^2 ...

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Byju's Answer

Standard XII

Mathematics

Property 6

If α̅ and ...

Question

If $¯ α$ and $¯ β$ are two vectors such that $∣ ∣ ¯ α + ¯ β ∣ ∣ < ∣ ∣ ¯ α - ¯ β ∣ ∣,$ then $¯ α$ and $\to β$ are inclined at

A right angle

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An obtuse angle

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An acute angle

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Parallel

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Solution

The correct option is B An obtuse angle
Given relation
$∣ ∣ \to α + \to β ∣ ∣ < ∣ ∣ \to α - \to β ∣ ∣$
On squaring both sides
$(∣ ∣ \to α + \to β ∣ ∣)^{2} < (∣ ∣ \to α - \to β ∣ ∣)^{2}$
${| \to α |}^{2} + {∣ ∣ \to β ∣ ∣}^{2} + 2 | \to α | ∣ ∣ \to β ∣ ∣ cos θ < {| \to α |}^{2} + {∣ ∣ \to β ∣ ∣}^{2} - 2 | \to α | ∣ ∣ \to β ∣ ∣ cos θ$
on cancel out ${| \to α |}^{2}, {∣ ∣ \to β ∣ ∣}^{2}$
$2 | \to α | ∣ ∣ \to β ∣ ∣ cos θ < - 2 | \to α | ∣ ∣ \to β ∣ ∣ cos θ$
$2 cos θ < 0$
$θ > {cos}^{- 1} 0$
$θ > 90^{.}$
i.e. obtuse angle

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If ¯α and ¯β are two vectors such that ∣∣¯α+¯β∣∣<∣∣¯α−¯β∣∣, then ¯α and →β are inclined at

If $¯ α$ and $¯ β$ are two vectors such that $∣ ∣ ¯ α + ¯ β ∣ ∣ < ∣ ∣ ¯ α - ¯ β ∣ ∣,$ then $¯ α$ and $\to β$ are inclined at