Q.

The angle between a line with direction ratios 2:2:1 and a line joining (3,1,4) to (7,2,12) is

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a

cos−1(2/3)

b

cos−1(−2/3)

c

tan−1(−2/3)

d

sin−1(2/3)

answer is A.

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Detailed Solution

D.R's = (2,2,1), and (7-3, 2-12, 12-4) = (2,2,1), (4,1,8)cosθ=a1a2+b1b2+c1c2a12+b12+c12a22+b22+c22=23∴θ=cos−123
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The angle between a line with direction ratios 2:2:1 and a line joining (3,1,4) to (7,2,12) is