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If θθ be the angle between any two vectors a→ and b→, then |a→⋅b→|=|a→×b→|, when θθ is equal to -

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Question

If `θ` be the angle between any two vectors `veca` and `vecb`, then `|veca * vecb| = |veca xx vecb|`, when `θ` is equal to

Options

  • 0

  • `pi/4`

  • `pi/2`

  • `pi`

MCQ

Solution

`pi/4`

Explanation:

'θ' is the angle between vectory `veca` and `vecb`

∴ `|veca * vecb| = |veca| |vecb| |cos theta|`

And `|veca xx vecb| = |veca| |vecb| |sin theta|`

We have `|veca * vecb| = |veca xx vecb|`

∴ `|veca||vecb| cos theta = |veca||vecb| sin theta`

⇒ `|cos theta| = |sin theta|`

or `|tan theta|` = 1 or `tan theta` = 1

⇒ `theta = pi/4`

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