A vector $\vec{a}$ has components $2 p$ and 1 with respect to a rectangular cartesian system. This s

Question

A vector $\vec{a}$ has components $2 p$ and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to the new system, $\vec{a}$ has component $p+1$ and 1 , then\

Professor PC Thomas Classes · Answer

(b) : Let $\vec{a}$ makes angle $\alpha$ with original $x$-axis\ Let the original co-ordinate system be rotated through angle $	heta$, and $|\vec{a}|=a$\ $2 p=a \cos \alpha, 1=a \sin \alpha$\ $p+1=a \cos (\alpha+	heta), 1=a \sin (\alpha+	heta)$