If the line joining the points A(2,0) and B(3,1) is rotated about A in anticlockwise direction throgh an angle of `15^@`, find the equation of the line in its new position.

A line through the point A (2, 0), which makes an angle of 30^@ with the positive direction of x-axis is rotated about A in clockwise direction through an angle 15^@ . Then the equation of the straight line in the new position is :

If the pair of lines sqrt(3)x^(2)-4xy+sqrt(3)y^(2)=0 is rotated about the origin by pi//6 in the anticlockwise sense , then find the equation of the pair of lines in the new position.

The plane x-y-z=4 is rotated through an angle 90^(@) about its line of intersection with the plane x+y+2z=4 . Then the equation of the plane in its new position is

A line perpendicular to the line segment joining the points (1,0) and (2,3) divides it in the ratio 1 : n. Find the equation of the line.

Two lines passing through the point (2, 3) intersect each other at an angle of 60^@ . If the slope of one line is 2, find the equation of the other line.

Find the projection of the line segment joining the points: (2,-3,0), (0,4,5) on the line with direction cosines

The length of perpendicular from the origin to a line is 9 and the line makes an angle of 120^(@) witth the positive direction of Y - axes . Find the equation of the line .

Find the equation of the plane through the points (2,2,-1) and (3,4,2) and parallel to the line whose direction ratios are .

Two lines passing through the point (2, 3) intersects each other at an angle of 60^@ . If slope of one line is 2, find equation of the other line.

Find the equation of the line joining the points A(0,-1,3) and B(2,-3,-1).