Find -a-b- if two vectors a- and b- are such that -a-2-b-3 and a-b-4

Given, |a|=2, |b|=3 and a.b=4 nbsp; We have, |a b|^2=|a|^2 2(a.b)+|b|^2 ⇒ |a b|^2= 2^2 2×4+3^2=5 ⇒ |a b|=√(5) ...

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Byju's Answer

Standard XII

Physics

Introduction

Find |a⃗-b⃗|,...

Question

Find $| \to a - \to b |$ , if two vectors $\to a$ and $\to b$ are such that $| \to a | = 2$ , $| \to b | = 3$ and $\to a . \to b = 4$

\sqrt{3}

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\sqrt{7}

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\sqrt{21}

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\sqrt{5}

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Solution

The correct option is D $\sqrt{5}$
Given, $| \to a | = 2$ , $| \to b | = 3$ and $\to a . \to b = 4$
We have,
${| \to a - \to b |}^{2} = {| \to a |}^{2} - 2 (\to a . \to b) + {| \to b |}^{2}$
$\Rightarrow {| \to a - \to b |}^{2} = 2^{2} - 2 \times 4 + 3^{2} = 5$
$\Rightarrow | \to a - \to b | = \sqrt{5}$

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Find |→a−→b|, if two vectors →a and →b are such that |→a|=2, |→b|=3 and →a.→b=4

The correct option is D √5Given, |→a|=2, |→b|=3 and →a.→b=4 We have, |→a−→b|2=|→a|2−2(→a.→b)+|→b|2 ⇒ |→a−→b|2=22−2×4+32=5 ⇒ |→a−→b|=√5

Find $| \to a - \to b |$ , if two vectors $\to a$ and $\to b$ are such that $| \to a | = 2$ , $| \to b | = 3$ and $\to a . \to b = 4$