Angle of a line with the positive direction of the x-axis is `theta` . The line is rotated about some point on it in anticlockwise direction by angle `45^0` and its slope becomes `3.` Find the angle `theta`

True or false: The angle formed by rotating a ray about its end point in anticlockwise direction is positive.

The magnitude of the angle which the line y=-x makes with the positive direction of the x axis is -

The line P Q whose equation is x-y=2 cuts the x-axis at P ,a n dQ is (4,2). The line P Q is rotated about P through 45^0 in the anticlockwise direction. The equation of the line P Q in the new position is

A straight line passes throught the point P(3,-2) and makes an angle theta with the positive direction of x - axis Find theta , given that the distance of P from the point of intersection of this line with the line 3x+4y=4 is (3sqrt(2))/(5) units.

A straight line passes through the point A(1,2) and makes an angle theta with the positive direction of x -axis . Find theta given that the distance of A from the point of intersection of this line with the line x+y=4 "is"(sqrt(6))/(3) unit.

A line which makes an acute angle theta with the positive direction of the x-axis is drawn through the point P(3,4) to meet the line x=6 at R and y=8 at Sdot Then,

A line makes an acute angle with the positive direction of x-axis and passes through the points (6, -7, -1) and (2, -3, 1), find the direction cosines of the line.

If the equation of the pair of straight lines passing through the point (1,1) , one making an angle theta with the positive direction of the x-axis and the other making the same angle with the positive direction of the y-axis, is x^2-(a+2)x y+y^2+a(x+y-1)=0,a!=2, then the value of sin2theta is

If a line makes an angle of pi/4 with the positive direction of each of x-axis and y-axis, then the angel that the line makes with the positive direction of the z-axis is a. pi/3 b. pi/4 c. pi/2 d. pi/6

The point (4,1) undergoes the following transformation successively (i) Reflection about the line y=x (ii) Translation through a distance 2 unit along the positive direction (x-axis) (iii)Rotation through on angle pi//4 about origin in anticlockwise direction. Then the co-ordinates of the final points