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.

Find the inclination of the straight line perpendicular to the straight line sqrt3x+y=1 .

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.

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.

Show that the points whose coordinates are (1,4) , (3,-2) and (-3,16) are on the same straight line . Write down the equation of the straight line on which the points lie Verify that this line is perpendicular to the line whose equation is 2x-6y+13=0 .

Find the equation of the straight line perpendicular to 2x+3y+5=0 and passing through the point (2,-3).

Let A(2,-6) and B(-3,-1) be two given points .Find the length of orthogonal projection of the line segment overline(AB) upon the straight line 3x+y=10.

Find the coordinates of the foot of the perpendicular drawn from the point (2,-5) on the straight line x=y+1.

Prove that the points (3,1), (5,-5) and (-1,13) are collinear . Find the equation of the straight line on which the points lie.

If l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) are direction cosines of two mutually perpendicular straight lines, then prove that the direction cosines of the straight line which is perpendicular to both the given lines are pm (m_(1)n_(2)-m_(2)n_(1)), pm (n_(1)l_(2)-n_(2)l_(1)), pm (l_(1)m_(2)-l_(2)m_(1))

Find the equation of the straight line passing through the point of intersection of the straight lines x+2y+3=0 and 3x+4y+7=0 and parallel to the straight line y=-(5)/(8)x .