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Question

Find the acute angle between the lines whose direction ratios are (5,12,13) and (3,4,5).

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Solution

a1=5,b1=12,c1=13
a2=3,b2=4,c2=5
Acute angle cosθ=∣ ∣a1a2+b1b2+c1c2a12+b12+c12a22+b22+c22∣ ∣
cosθ=15486525+144+1699+16+25
cosθ=98132×5×2
cosθ=9813×5×2
cosθ=4965
cosθ=4965θ=cos1(4965)

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