The vector ` vec a` has the components `2p` and 1 w.r.t. a rectangular Cartesian system. This system is rotated through a certain angel 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 rotted through an angel alpha about the origin 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.

Each question has four choices a, b, c, and d, out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2. a. Both the statements are TRUE and statement 2 is the correct explanation for Statement 1. b. Both the statements are TRUE but Statement 2 is NOT the correct explanation for Statement 1. c. Statement 1 is TRUE and Statement 2 is FALSE. d. Statement 1 is FALSE and Statement 2 is TRUE. A vector has components p and 1 with respect to a rectangular Cartesian system. The axes are rotted through an angel alpha about the origin 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 origin vector and the new vector remains the same.

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 of coordinates are rotated about the z-axis though an angle of pi//4 in the anticlockwise direction and the components of a vector are 2 sqrt(2), 3 sqrt(2), 4. Prove that the components of the same vector in the original system are -1,5,4.

If vec r is a vector of magnitude 21 and has direction ratios 2,-3a n d6, then find vec rdot

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 a. (-3)/4 b. 1/4 c. 3/4 d. 1/2

Let vec a , vec b a n d vec c be three vectors having magnitudes 1, 5and 3, respectively, such that the angel between vec aa n d vec bi stheta and vec axx( vec axx vec b)=c . Then t a ntheta is equal to a. 0 b. 2/3 c. 3/5 d. 3/4

If theta is th angel between the unit vectors a and b , then prove that cos(theta/2)=1/2| vec a+ vec b| .,, sin(theta/2)=1/2| vec a- vec b|

Let Aa n dB are events of an experiment and P(A)=1//4, P(AuuB)=1//2, then value of P(B//A^c) is a. 2//3 b. 1//3 c. 5//6 d. 1//2