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, and `theta and Phi` are acute angles , then

Let P M be the perpendicular from the point P(1,2,3) to the x-y plane. If vec O P makes an angle theta with the positive direction of the z- axis and vec O M makes an angle phi with the positive direction of x- axis, w h e r eO is the origin and thetaa n dphi are acute angels, then a. costhetacosphi=1//sqrt(14) b. sinthetasinphi=2//sqrt(14) c. ""tanphi=2 d. tantheta=sqrt(5)//3

Let PN be the perpendicular from the point P(1, 2, 3) to xy-plane. If OP makes an angle alpha with positive direction of the z-axis and ON makes an angle beta with the positive direction of x-axis, where O is the origin ( alpha and beta are acute angles), then

Let P M be the perpendicular from the point P(1,2,3) to the x-y plane. If vec O P makes an angle theta with the positive direction of the z- axis and vec O M makes an angle varphi with the positive direction of x- axis, w h e r eO is the origin and thetaa n dvarphi are acute angels, then a. costhetacosvarphi=1//sqrt(14) b. sinthetasinvarphi=2//sqrt(14) c. ""tanvarphi=2 d. tantheta=sqrt(5)//3

Let PQ be the perpendicular form P(1,2,3) to xy-plane. If OP makes an angle theta with the positive direction of z-axis and OQ makes an angle phi with the positive direction of x-axis where O is the origin show that tantheta=sqrt(5)/3 and tanphi=2 .

If a line makes an angle of pi/4 with the positive directions of each of x-axis and y-axis, then the angle that the line makes with the positive direction of z-axis is

Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.

Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.

If O be the origin and OP=r and OP makes an angle theta with the positive direction of x-axis and lies in the XY plane find the coordinates of P.

Find the equation of a line through the origin which makes an angle of 45^0 with the positive direction of x-axis.

The length of the perpendicular from the origin to a line is 7 and a line makes an angle of 150^@ with the positive direction of x -axis . then the equation of the line is: