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 z=sqrt(2)- isqrt(2) si rotated through an angle 45^(@) in the anti-clockwise direction about the origin, then the co-ordianates of its new position are

If (1)/(2),(1)/(sqrt(2)) a are the direction cosines of some vector, then find a.

A line segment has length 63 and direction ratios are 3, -2, 6. The components of the line vector are

Verify whether the ratios are direction cosines of some vector or not. (1)/(sqrt(2)),(1)/(2),(1)/(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.

If the pair of lines sqrt(3)x^2-4x y+sqrt(3)y^2=0 is rotated about the origin by pi/6 in the anticlockwise sense, then find the equation of the pair in the new position.