Let `epsilon_1 and epsilon_2` be the angles made by `vecA and -vecA` with the positive XD-axis. Show that `tanepsilon_1 = tanepsilon_2`. Thus giving `tanepsilon` does not uniquely determine of `vecA`.

The angle made by the vector vecA=2hati+2hatj with x-axis is

The angle made by the vector vecA=2hati+3hatj with Y-axis is

Find the angle of vector veca=6hati+2hatj-3hatk with x -axis.

Let L be the line of intersection of the planes 2x+3y+z=1 and x+3y+2z=2 . If L makes an angle alpha with the positive X=axis, then cosalpha equals

Find the angle between two vectors vecaandvecb with magnitudes 1 and 2 respectively and when veca*vecb=1 .

Let PM be the perpendicular from the point P(1, 2, 3) to XY-plane. If OP makes an angle theta with the positive direction of the Z-axies and OM makes an angle Phi with the positive direction of X-axis, where O is the origin, then find theta and Phi .

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 (a) a-2 (b) a+2 (c) 2/(a+2) (d) 2/a

A player throwsa a ball upwards with an initial speed of 29.4 ms^(-1) . (i) What is the direction of acceleration during the upwared motion of the ball? (ii) What are the velocity and acceleration of the ball at the highest point of its motion? (iii) Choose the x=0 and t=0 to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of X-axis, and give the signs of positive, velocity and acceleration of the ball during its upward, and downward motion. (iv) To what height does the ball rise and after how long does the ball return to the player's hand?( Take g =9.8 ms^(-2) , and neglect air resistance).

A player throws a ball upwards with an initial speed of 29.4 ms^(-1) (a) What is the direction of acceleration during the upward motion of the ball ? (b) What are the velocity and acceleration of the ball at the highest point of its motion ? (c) Choose the x = 0 m and t=0 s to be the location and time of the ball at its highest point vertically downward direction to be the positive direction of x-axis and give the signs of position, velocity and acceleration of the ball during its upward and downward motion. (d) To what height does the ball rise and after how long does the ball return to the player's hands ? (Take g = 9.8 ms^(-2) and neglect air resistance).

Let -1lt=plt=1 . Show that the equation 4x^3-3x-p=0 has a unique root in the interval [1/2,1] and identify it.