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प्रश्न
Find `bar"u".bar"v"` if `|bar"u"| = 2, |bar"v"| = 5, |bar"u" xx bar"v"| = 8`
उत्तर
Let θ be the angle between `bar"u"` and `bar"v"`
Then `|bar"u" xx bar"v"| = 8` gives
`|bar"u"||bar"v"|` sin θ = 8
∴ 2 × 5 × sin θ = 8
∴ sin θ = `4/5`
cos θ = `+- sqrt(1 - "sin"^2theta)` ...[∵ 0 ≤ θ ≤]
`= - sqrt(1 - (4/5)^2)`
`= +-sqrt(1 - 16/25)`
`= - sqrt(9/25) = +-3/5`
Now, `bar"u".bar"v" = |bar"u"||bar"v"|` cos θ
∴ `bar"u".bar"v" = 2 xx 5 xx (+- 3/5) = +- 6`
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