If a-b- and c- are unit vectors such that a- -b- -c- -0- then the angle between a- and b- is

The correct option is A 2π3 We have, a⃗ +b⃗ +c⃗ =0 ⇒a⃗+b⃗= c⃗ Now square both sides, ⇒ (a⃗+b⃗)^2=( c⃗)^2 ⇒ |a⃗|^2+|b⃗|^2+2a⃗·b⃗=|c⃗|^2 ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

If a⃗,b⃗ an...

Question

If $\to a, \to b$ and $\to c$ are unit vectors such that $\to a + \to b + \to c = 0$ , then the angle between $\to a$ and $\to b$ is

\frac{2 π}{3}

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\frac{π}{2}

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\frac{π}{3}

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\frac{π}{4}

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Solution

The correct option is A $\frac{2 π}{3}$
We have, $\to a + \to b + \to c = 0$
$\Rightarrow \to a + \to b = - \to c$
Now square both sides,
$\Rightarrow (\to a + \to b)^{2} = (- \to c)^{2}$
$\Rightarrow | \to a |^{2} + | \to b |^{2} + 2 \to a \cdot \to b = | \to c |^{2}$
$\Rightarrow 1 + 1 + 2 | \to a | | \to b | cos θ = 1$ , $θ$ is angle between $\to a$ and $\to b$
$\Rightarrow 1 + 1 + 2 (1) (1) | cos θ = 1$
$\Rightarrow cos θ = - \frac{1}{2}$
$∴ θ = \frac{2 π}{3}$

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If →a,→b and →c are unit vectors such that →a+→b+→c=0, then the angle between →a and →b is

The correct option is A 2π3We have, →a+→b+→c=0⇒→a+→b=−→cNow square both sides,⇒(→a+→b)2=(−→c)2⇒|→a|2+|→b|2+2→a⋅→b=|→c|2⇒1+1+2|→a||→b|cosθ=1, θ is angle between →a and →b⇒1+1+2(1)(1)|cosθ=1⇒cosθ=−12∴θ=2π3

If $\to a, \to b$ and $\to c$ are unit vectors such that $\to a + \to b + \to c = 0$ , then the angle between $\to a$ and $\to b$ is