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Question
Find the angle between the lines `vecr = 3hati - 2hatj + 6hatk + lambda(2hati + hatj + 2hatk)` and `vecr = (2hatj - 5hatk) + mu(6hati + 3hatj + 2hatk)`
Solution
Here `vecb_1 = 2hat"i" + hat"j" + 2hat"k"` and `vecb_2 = 6hat"i" + 3hat"j" + 2hat"k"`
So, `cos theta = (vecb_1 * vecb_2)/(|vecb_1||vecb_2|)`
= `((2hati + hatj + 2hatk)*(6hati + 3hatj + 2hatk))/(sqrt((2)^2 + (1)^2 + (2)^2) * sqrt((6)^2 + (3)^2 + (2)^2)`
= `(12 + 3 + 4)/(sqrt(4 + 1 + 4) * sqrt(36 + 9 + 4))`
= `19/(sqrt(9)*sqrt(49))`
= `19/(3*7)`
= `19/21`
∴ `theta = cos^-1(19/21)`
Thus, the angle between the lines is `cos^-1(19/21)`.
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