Question

Find the angle between p and q if both of them are unit vector and p - q is also a unit vector
. A. TU/5 B. TT/2 C. Tt/3 D. TT/4​

Answer 1

Answer:

thank you for giving me point

sorry I want point sorry

Answer 2

Given two unit vectors and their difference vector is also a unit vector, find the angle between the vector.

Explanation:

• Let there exist two vectors denoted by 'A' and 'B' respectively.
• If the angle between them is denoted by theta. Then the scalar product or dot product of these vectors is given by,   $->(\vec A).(\vec B)=|\vec A||\vec B|cos\theta$    ---(a)
• Let the vector $(\vec p-\vec q)$ be denoted another vector 'c'.
• Now here we have, $|\vec p|=|\vec q |=|\vec c|=1$
• Hence from (a) taking dot product of the 'c' with itself we get, $\vec c=\vec p-\vec q\\(\vec c).(\vec c)=(\vec p-\vec q).(\vec p-\vec q) \\->|\vec c|^2cos0=|\vec p|^2cos0+|\vec q|^2cos0-2|\vec p||\vec q|cos\theta\\->|\vec c|^2=|\vec p|^2+|\vec q|^2-2|\vec p||\vec q|cos\theta\\->1=1+1-2cos\theta\\->cos\theta=\frac{1}{2} \\->\theta=\frac{\pi}{3}$  
• Hence, the angle between the given unit vectors 'p' and 'q' is (c) $\frac{\pi }{3}$.