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Question
Find `|bar"u" xx bar"v"|` if `|bar"u"| = 10, |bar"v"| = 2, bar"u".bar"v" = 12`
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
The answer in the textbook is incorrect.
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