Question
Let p =2 i + j +3 k and q = i - j + k . If for some real numbers , , and , we have 15 i +10 j +6 k = (2 p + q )+ ( p -2 q )+ ( p q ) then the value of is
JEE Advanced
Mathematics
Vector Algebra
2024
JEE Advanced 2024 (Paper 2)
JEE Advanced Mathematics Question (2024) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
15 i +10 j +6 k = (2 p + q )+ ( p -2 q )+ ( p q ) taking dot with ( p q ) | array ccc 15 & 10 & 6 \\ 2 & 1 & 3 \\ 1 & -1 & 1 array |=0+0+ ( p ^2 q ^2-( p q )^2 ) [ ( p q )^2+( p q )^2= p ^2 q ^2 ] aligned & 52=26 \\ & =2 aligned
Related: Mathematics — Vector Algebra · All PYQ Banks