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प्रश्न
If `bar"a".bar"b" = sqrt3` and `bar"a" xx bar"b" = 2hat"i" + hat"j" + 2hat"k"`, find the angle between `bar"a"` and `bar"b"`.
उत्तर
Let θ be the angle between `bar"a"` and `bar"b"`
∵ `bar"a" xx bar"b" = 2hat"i" + hat"j" + 2hat"k"`
∴ `|bar"a" xx bar"b"| = sqrt(2^2 + 1^2 + 2^2) = sqrt(4 + 1 + 4) = 3`
∴ `|bar"a"||bar"b"|` sin θ = 3 ...(1)
∴ `bar"a".bar"b" = sqrt3`
∴ `|bar"a"||bar"b"| "cos" theta = sqrt3` ....(2)
∴ Dividing (1) by (2), we get
`(|bar"a"||bar"b"| "sin" theta)/(|bar"a"||bar"b"| "cos" theta) = 3/sqrt3`
∴ tan θ = `sqrt3 = tan 60^circ`
∴ θ = 60°
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