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Question
If `bar"p", bar"q"` and `bar"r"` are unit vectors, find `bar"p".bar"r".`
Solution
Let the triangle be denoted by ABC, where `bar"AB" = bar"p"`, `bar"AC" = bar"q"` and `bar"BC" = bar"r"`
∵ `bar"p", bar"q", bar"r"` are unit vectors.
∴ l(AB) = l(BC) = l(CA) = 1
∴ the triangle is equilateral
∴ ∠A = ∠B = ∠C = 60°
Using the formula for angle between two vectors,
cos B = `(bar"p".bar"r")/(|bar"p"|.|bar"r"|)`
we get `bar"p".bar"r" = 1/2`
∴ cos 60° = `(bar"p".bar"r")/(1 xx 1)`
∴ `1/2 = bar"p".bar"r"`
∴ `bar"p".bar"r" = 1/2`
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