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Addition of Vectors

If a+b+c=0,...

Question

If $a + b + c = 0, | a | = 3, | b | = 5, | c | = 7,$ then the angle between a and b is

π / 6

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2 π / 3

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5 π / 3

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π / 3

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Solution

The correct option is D $π / 3$
Given $\to a + \to b + \to c = 0$ and $| \to a | = 3, | \to b | = 5, | \to c | = 7$

let angle between $\to a$ and $\to b$ be $θ$

$\to a + \to b + \to c = 0$

$\Rightarrow \to a + \to b = - \to c$

$\Rightarrow | \to a |^{2} + | \to b |^{2} + 2 \to a \cdot \to b = | \to c |^{2}$

$\Rightarrow 9 + 25 + 30 cos θ = 49$

$\Rightarrow cos θ = \frac{1}{2}$

$∴ θ = \frac{π}{3}$

Hence, option D.

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If a+b+c=0,|a|=3,|b|=5,|c|=7, then the angle between a and b is

The correct option is D π/3Given →a+→b+→c=0 and |→a|=3,|→b|=5,|→c|=7let angle between →a and →b be θ→a+→b+→c=0⇒→a+→b=−→c⇒|→a|2+|→b|2+2→a⋅→b=|→c|2⇒9+25+30cosθ=49⇒cosθ=12∴θ=π3Hence, option D.

If $a + b + c = 0, | a | = 3, | b | = 5, | c | = 7,$ then the angle between a and b is