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Find the shortest distance between two lines whose vector equations are `vec(r) = (hat(i) + 2 hat(j) + 3 hat(k))+lambda(hat(i)- 3hat(j) + 2 hat(k)) and vec(r) = (4 hat(i) + 5 hat(j) + 6 hat(k))+ mu (2 hat(i)+3 hat(j) + hat(k))`.

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The correct Answer is:
` = (3)/(sqrt(19)) or (3 sqrt(19))/(19)`
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Find the shortest distance between the lines whose vector equations are vec(r) = (hat(i) + hat(j)) + lambda(2 hat(i) - hat(j) + hat(k)) and vec(r) = (2 hat(i) + hat(j) - hat(k)) + mu (3 hat(i) - 5 hat(j)+2 hat(k)) .

Find the distance between the lines overset(to)(r ) = hat(i) + 2 hat(j) - 4 hat(k) + lambda ( 2 hat(i) + 3 hat(j) + 6 hat(j) ) & overset(to)(r ) = 3 hat(i) + 3 hat(j) - 5 hat(k) + mu ( -2 hat(i) + 3 hat(j) + 8 hat(k) )

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Find the equation of the plane passing through the point P(1,1,1) and containing the line vec(r) = (-3 hat(i) + hat(j) + 5 hat(k)) + lambda (3 hat(i) - hat(j) - 5 hat(k)) . Also, show that the plane contains the line vec(r) = (- hat(i) + 2 hat(j) + 5hat(k)) + mu (hat(i) - 2 hat(j) - 5 hat(k)) .

Find the angle between the vectors vec(a) = hat(i) + hat(j) + hat(k) and vec(b) = hat(i) - hat(j) + hat(k) .

Find the magnitude of the vector (2hat(i) - 3hat(j) - 6hat(k)) + (-hat(i) + hat(j) + 4hat(k)) .

Find the shortest distance between the lines. r=(hat(i)+2hat(j)+hat(k))+lambda(hat(i)-hat(j)+hat(k)) " and " r=(2hat(i)-hat(j)-hat(k))+mu(2hat(i)+hat(j)+2hat(k)) .

OSWAAL PUBLICATION-THREE DIMENSIONAL GEOMETRY-Topic -2 (Short answer type questions-II)
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  17. Find the shortest distance between the following pair of lines : (...

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  18. 2/ Find the perpendicular distance of the point (1, 0, 0) from the lin...

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  20. Find the angle between the following pair of lines: (-x+2)/(-2)=(y-...

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