Let A(2, -3, -1), B(4, 5, 2), C(-3, 4, 1) and D(2, 3, 5) are four given points. Find direction cosines of a straight line which is perpendicular to both the straight line AB and CD.

Find the direction cosines of the line which is perpendicular to the lines with direction ratios 4, 1, 3 and 2, -3, 1 .

If O is the origin and A(2, 3, 1), B(1, 1, -5) are two given points then show that the straight line OA is perpendicular to the straight line OB.

Can the numbers 1, 2, 3 be the direction cosines of a straight line?

Let l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) be the direction ratios of two given straight lines. Find the direction ratios of a straight line which is perpendicular to both the given straight lines.

Let A(-2, 0, 3), B(0, 3, -3), C(3, 3, 5) and D(5, 4, 3) be four given points, find the acute angle between the lines AB and CD.

If points A (2, 4, 0), B(3, 1, 8), C(3, 1, -3), D(7, -3, 4) are four points then projection of line segment AB on line CD.

If points A (2, 4, 0), B(3, 1, 8), C(3, 1, -3), D(7, -3, 4) are four points then projection of line segment AB on line CD.

Find the equation of a straight line that has y- intercept 4 and is perpendicular to straight line joining (2,-3) and (4.2)

The direction cosines of two lines are 1, -2,-2 and 0, 2, 1. Find the direction cosines of the line which is perpendicular to both the lines,