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.

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 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

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.

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

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

The position vectors particle has length 1m and makes 30^(@) with the x-axis. What are the lengths of the x and y components of the position vector?

Two vectors have magnitudes 3 unit and 4 unit respectively. What should be the angel between them if the magnitude of the resultant ils a. 1 unit, b. 5 unit and c. 7 unit.