Given that A - B - C- If - A -4- B -5 and - C -61- then angle between A and B is-A- 30-B- 60-C- 120-D- 90-

The correct option is B 60^∘Applying the formula for addition of vectors: √(|A|^2+|B|^2+2|A||B|cosθ)=|C| Squaring both sides, |A|^2+|B|^2+2|A||B|cosθ=|C|^2 4^ ...

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Byju's Answer

Standard XII

Physics

Vector Addition

Given that A ...

Question

Given that $\to A + \to B = \to C$ . If $| \to A | = 4, | \to B | = 5$ and $| \to C | = \sqrt{61}$ , then angle between $\to A$ and $\to B$ is:

30^{\circ}

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60^{\circ}

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90^{\circ}

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120^{\circ}

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Solution

The correct option is B $60^{\circ}$
Applying the formula for addition of vectors:
$\sqrt{{| \to A |}^{2} + {| \to B |}^{2} + 2 | \to A | | \to B | cos θ} = | \to C |$
Squaring both sides,
${| \to A |}^{2} + {| \to B |}^{2} + 2 | \to A | | \to B | cos θ = {| \to C |}^{2}$

$4^{2} + 5^{2} + (2 \times 4 \times 5 cos θ) = 61$
$\Rightarrow 40 cos θ = 41 - 21 = 20$
or, $cos θ = 1 / 2$
$∴ θ = 60^{\circ}$

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Given that →A+→B=→C. If |→A|=4,|→B|=5 and |→C|=√61, then angle between →A and →B is:

The correct option is B 60∘Applying the formula for addition of vectors: √|→A|2+|→B|2+2|→A||→B|cosθ=|→C| Squaring both sides, |→A|2+|→B|2+2|→A||→B|cosθ=|→C|2 42+52+(2×4×5cosθ)=61 ⇒40cosθ=41−21=20 or, cosθ=1/2 ∴θ=60∘

Given that $\to A + \to B = \to C$ . If $| \to A | = 4, | \to B | = 5$ and $| \to C | = \sqrt{61}$ , then angle between $\to A$ and $\to B$ is: