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Question

Find the angle between two lines whose direction ratio are
(i) 2,1,2 and 4,8,1 (ii) 5,12,13 and 3,4,5

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Solution

Angle between two lines whose direction ratios are:
a1,b1,c1 and a2,b2,c2 is
cosθ=∣ ∣ ∣a1a2+b1b2+c1c2a21+b21+c21+a22+b22+c22∣ ∣ ∣
(1) a1=2,b1=1,c2=2;
a2=4,b2=8,c2=1
cosθ=|8+8+2|4+1+46+64+1
cosθ=183×9
cosθ=23
θ=cos1(23)
(2) a1=5,b2=12, c1=13, a2=3, b2=4, c2=5
cosθ=|1548+65|35+144+1699+16+25
cosθ=|2|13252
cosθ=165
θ=cos1(165).

1116328_1157214_ans_1f0ed704756d4ce3aae9ab531aebdfb9.jpg

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