InterviewSolution
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InterviewSolution
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Find the angle between thepair of lines given by ` -> r=3 hat i+2 hat j-4 hat k+lambda( hat i+2 hat j+2 hat k)`and` -> r=5 hat i-2 hat j+mu(3 hat i+2 hat j+6 hat k)`. |
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Answer» Let `theta` be the angle between the given lines. The given lines are parallel to the vectors. `bar(b_(1))=hat(i)+2hat(j)+2hat(k) and bar(b_(2))=3hat(i)+2hat(j)+6hat(k)` respectively. `:.` The angle `theta` is given by `cos theta =(bar(b_(1))*bar(b_(2)))/(|bar(b_(1))|*|bar(b_(2))|)` `bar(b_(1))*bar(b_(2))=(hat(i)+2hat(j)+2hat(k))*(3hat(i)+2hat(j)+6hat(k))` `1xx3+2xx2+2xx6` `=3+4+12=19` `bar(b_(1))=sqrt(1^(2)+2^(2)+2^(2))` `=sqrt(9)=3` `bar(b_(2))=sqrt(3^(2)+2^(2)+6^(2))` `=sqrt(9+4+36)=sqrt(49)=7` `:. cos theta = (19)/(3xx7)=(19)/(21)` `:.theta=cos^(-1)((19)/(21))` |
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