Question
Mathematics Question on Quadratic Equations
If a→=i^+2j^−3k^, b→=3i^−j^+2k^ then the angle between a→+b→,a→−b→ is:
A
(A) 0∘
B
(B) 180∘
C
(C) 90∘
D
(D) −180∘
Answer
(C) 90∘
Explanation
Solution
Explanation:
Given:a→=i^+2j^−3k^b→=3i^−j^+2k^So,(a→+b→)=i^+2j^−3k^+3i^−j^+2k^(a→+b→)=(i^+3i^)+(2j^−j^)+(−3k^+2k^)a→+b→=4i^+j^−k^(a→−b→)=i^+2j^−3k^−3i^−j^+2k^(a→−b→)=(i^−3i^)+(2j^−(−j)^)+(−3k^−2k^)⇒a→−b→=−2i^+3j^−5k^Then,(a→+b→)⋅(a→−b→)=(4i^+j^−k^)⋅(−2i^+3j^−5k^)(a→+b→)⋅(a→−b→)=−8+3+5=0If (a→+b→)⋅(a→−b→)=0Then angle between two vectors is 90∘.Hence, the correct option is (C).