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Find uv|u¯×v¯| if uvuv|u¯|=10,|v¯|=2,u¯.v¯=12 - Mathematics and Statistics

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Sum

Find `|bar"u" xx bar"v"|` if `|bar"u"| = 10, |bar"v"| = 2, bar"u".bar"v" = 12`

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Solution

Let θ be the angle between `bar"u"` and `bar"v"`

Then `bar"u".bar"v" = 12` gives

`|bar"u"||bar"v"|` cos θ = 12

∴ 10 × 2 × cos θ = 12

∴ cos θ = `3/5`  where `0<= theta <= pi/2`

sin θ = `sqrt(1 - "cos"^2theta)`   

`= sqrt(1 - (3/5)^2)`

`= sqrt(1 - 9/25)`

`= sqrt(16/25) = 4/5`

Now, `|bar"u" xx bar"v"| = |bar"u"||bar"v"|` sin θ

∴ `bar"u".bar"v" = 10 xx 2 xx (4/5) = 16`

Notes

[Note: Answer in the textbook is incorrect.]

Concept: Vector Product of Vectors (Cross)
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