The vector ` vec a` has the components `2p` and 1 w.r.t. a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counterclockwise sense. If, with respect to a new system, ` vec a` has components `(p+1)a n d1` , then `p` is equal to
a. `-4` b. `-1//3` c. `1` d. `2`

A vector has components p and 1 with respect to a rectangular Cartesian system. The axes are rotated through an angle alpha about the origin in the anticlockwise sense. Statement 1: If the vector has component p+2 and 1 with respect to the new system, then p=-1. Statement 2: Magnitude of the original vector and new vector remains the same.

When a right handed rectangular Cartesian system OXYZ is rotated about the z-axis through an angle pi/4 in the counter-clockwise, direction it is found that a vector veca has the component 2sqrt(3), 3sqrt(2) and 4.

A vector a has components a_1,a_2,a_3 in a right handed rectangular cartesian coordinate system OXYZ the coordinate axis is rotated about z axis through an angle pi/2 . The components of a in the new system

A vector has component A_1, A_2a n dA_3 in a right -handed rectangular Cartesian coordinate system O X Y Zdot The coordinate system is rotated about the x-axis through an angel pi//2 . Find the component of A in the new coordinate system in terms of A_1, A_2, a n dA_3dot

The axes are rotated through an angle pi//3 in the anticlockwise direction with respect to (0,0) . Find the coordinates of point (4,2) (w.r.t. old coordinate system) in the new coordinates system.

The components of a vector along the x- and y- directions are (n+1) and 1, respectively. If the coordinate system is rotated by an angle theta=60^(@) , then the components change to n and 3. The value of n is

Vectors drawn the origin O to the points A , Ba n d C are respectively vec a , vec ba n d vec4a- vec3bdot find vec A Ca n d vec B Cdot

If vec aa n d vec b are two unit vectors incline at angle pi//3 , then { vec axx( vec b+ vec axx vec b)}dot vec b is equal to (-3)/4 b. 1/4 c. 3/4 d. 1/2

Write a unit vector in the direction of vec P Q ,\ w h e r e\ P\ a n d\ Q are the points (1, 3, 0) and (4, 5, 6) respectively.

If vec n is a vector of magnitude sqrt(3) and is equally inclined with an acute angle with the coordinate axes. Find the vector and Cartesian forms of the equation of a plane which passes through (2, 1, -1) and is normal to vec n .