Question
107. u and v are two non-collinear unit vectors such that | u + v 2 + u v |=1. Then the value of | u v | is equal to
BITSAT
Mathematics
Vector Algebra
2022
BITSAT 2022
BITSAT Mathematics Question (2022) — Solution
Options
- A. | u + v 2 |
- B. | u + v |
- C. | u - v |
- D. | u - v 2 |
Answer
D. | u - v 2 |
Step-by-step solution
Given that, | u + v 2 + u v |=1 array ll & | u + v 2 + u v |^2=1 \\ & 2+2 4 + ^2 =1 \\ & [ u ( u v )= v ( u v )=0] \\ & ^2 2 = 2 \\ & =n 2 , n z \\ & = 2 3 array | u v |= 2 3 = 3 = | u - v 2 |
Related: Mathematics — Vector Algebra · All PYQ Banks