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Sum

If `|bar"a".bar"b"| = |bar"a" xx bar"b"|` and `bar"a".bar"b" < 0`, then find the angle between `bar"a" "and" bar"b"`.

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#### Solution

Let θ be the angle between `bar"a"` and `bar"b"`

Then `|bar"a".bar"b"| = |bar"a" xx bar"b"|` gives

`|"ab cos" theta| = |"ab sin" theta|`

∴ - ab cos θ = ab sin θ

∴ - 1 = tan θ

∴ tan θ = - tan `pi/4` = tan `(pi - pi/4)`

∴ tan θ = tan `(3pi)/4`

∴ `theta = (3pi)/4`

Hence, the angle between `bar"a"` and `bar"b"` is `(3pi)/4`.

Concept: Vector Product of Vectors (Cross)

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