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Angle between Two Planes

Let a and b b...

Question

Let $\to a$ and $\to b$ be two non-parallel unit vectors in a plane. If the vectors $(α \to a + \to b)$ bisects the internal angle between $\to a$ and $\to b$ , then $α$ is

A

\frac{π}{2}

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B

1

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C

2

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D

4

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Solution

The correct option is B $1$
$\to c = t ⎛ ⎜ ⎝ \frac{\to a}{| \to a |} + \frac{\to b}{| \to b |} ⎞ ⎟ ⎠$
$α \to a + \to b = t ⎛ ⎝ \frac{\to a}{1} + \frac{\to b}{1} ⎞ ⎠$
Since $| \to a | = | \to b | = 1$
On comparing we get,
$α = t$ and $t = 1$
Hence $α = 1$

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Angle between Two Planes

Standard XII Mathematics

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