Question
If a is a vector of magnitude 50 , collinear with the vector b =6 i -8 j - 15 2 k and makes an acute angle with the positive direction of Z - axis, then a is equal to
BITSAT
Mathematics
Vector Algebra
2021
BITSAT 2021
BITSAT Mathematics Question (2021) — Solution
Options
- A. -24 i +32 j +30 k
- B. 24 i -32 j -30 k
- C. -12 i +16 j -15 k
- D. 12 i -16 j -15 k
Answer
A. -24 i +32 j +30 k
Step-by-step solution
Since a =m b for some scalar m i.e., array l a =m (6 i -8 j - 15 2 k ) \\ |a|=|m| 36+64+ 225 4 \\ 50= 25 2 |m| \\ |m|=4 \\ m= 4 array Since, a makes an acute angle with the positive direction of Z - axis, so its z component must be positive and hence, m must be -4. a=-4 (6 i +8 j - 15 2 k )=-24 i +32 j +30 k
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