If a- and b- are unit vectors and - is the angle between them- then a- -b- is a unit vector when cos- -

The correct option is A 1 2 |a⃗+b⃗|^2=1 = gt; (a⃗+b⃗).(a⃗+b⃗)=1 = gt; |a⃗|^2+|b⃗|^2+2a⃗.b⃗=1 = gt; 2|a⃗||b⃗|cosα= 1 = gt; ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

If a⃗ and ...

Question

If $\to a$ and $\to b$ are unit vectors and $α$ is the angle between them, then $\to a + \to b$ is a unit vector when $cos α =$

- \frac{1}{2}

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\frac{1}{2}

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- \frac{\sqrt{3}}{2}

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\frac{\sqrt{3}}{2}

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Solution

The correct option is A $- \frac{1}{2}$
$| \to a + \to b |^{2} = 1$
=> $(\to a + \to b) . (\to a + \to b) = 1$
=> $| \to a |^{2} + | \to b |^{2} + 2 \to a . \to b = 1$
=> $2 | \to a | | \to b | c o s α = - 1$
=> $c o s α = \frac{- 1}{2}$

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If →a and →b are unit vectors and α is the angle between them, then →a+→b is a unit vector when cosα=

The correct option is A −12|→a+→b|2=1=> (→a+→b).(→a+→b)=1=> |→a|2+|→b|2+2→a.→b=1=> 2|→a||→b|cosα=−1=> cosα=−12

If $\to a$ and $\to b$ are unit vectors and $α$ is the angle between them, then $\to a + \to b$ is a unit vector when $cos α =$

The correct option is A $- \frac{1}{2}$
$| \to a + \to b |^{2} = 1$
=> $(\to a + \to b) . (\to a + \to b) = 1$
=> $| \to a |^{2} + | \to b |^{2} + 2 \to a . \to b = 1$
=> $2 | \to a | | \to b | c o s α = - 1$
=> $c o s α = \frac{- 1}{2}$