Question

A vector has components 2p and 1 with respect to a rectangular cartesian system. The system is rotated through a certain angle about the origin in the anti-clockwise sense. If a has components p + 1 and 1 with respect to the new system, then find p.​

Answer 1

✔ Explanation :-

✔ Solution :-

If x, y are the original components; X, Y the new components and α is the angle of rotation, then x = X cosα − Y sinα and y = X sinα + Y cosα

Therefore, 2p = (p + 1) cosα − sinα and 1 = (p + 1) sinα + cosα

Squaring and adding, we get 4p² + 1 = (p + 1)² + 1

⇒ p + 1 = ± 2p

⇒ p = 1 or −1 / 3

Hence,

• The value of p is 1 & -1/3.