Question

If `|vec"a" xx vec"b"|^2 + |vec"a".vec"b"|^2` = 144 and `|vec"a"|` = 4, then `|vec"b"|` is equal to ______.

Answer 1

If `|vec"a" xx vec"b"|^2 + |vec"a".vec"b"|^2` = 144 and `|vec"a"|` = 4, then `|vec"b"|` is equal to 3.

Explanation:

`|vec"a" xx vec"b"|^2 + |vec"a".vec"b"|^2` = 144

⇒ `(|vec"a"||vec"b"|| sin theta)^2 + (|vec"a"||vec"b"| cos theta)^2` = 144

⇒ `|vec"a"|^2 |vec"b"|^2 sin^2theta + |vec"a"|^2 |vec"b"|^2 cos^2theta` = 144

⇒ `|vec"a"|^2 |vec"b"|^2 (sin^2theta + cos^2theta)` = 144

⇒ `|vec"a"|^2 |vec"b"|^2` = 12

⇒ `4 * |vec"b"|` = 12

⇒ `|vec"b"|` = 3

Hence, the value of the filler is 3.