If \vec{a}=\hat{i}-\hat{j}+3\hat{k}, \,\vec{b}=5\hat{i}-2\hat{j}+\hat{k} \,and \,\vec{c}=\hat{i}-\hat{j} are such that \vec{a}+μ\vec{b} is perpendicular to \vec{c}, then the value of μ.

Category: QuestionsIf \vec{a}=\hat{i}-\hat{j}+3\hat{k}, \,\vec{b}=5\hat{i}-2\hat{j}+\hat{k} \,and \,\vec{c}=\hat{i}-\hat{j} are such that \vec{a}+μ\vec{b} is perpendicular to \vec{c}, then the value of μ.
Editor">Editor Staff asked 11 months ago

If \vec{a}=\hat{i}-\hat{j}+3\hat{k}, \,\vec{b}=5\hat{i}-2\hat{j}+\hat{k} \,and \,\vec{c}=\hat{i}-\hat{j} are such that \vec{a}+μ\vec{b} is perpendicular to \vec{c}, then the value of μ.
 
(a) \frac{7}{2}
 
(b) –\frac{7}{2}
 
(c) –\frac{3}{2}
 
(d) \frac{7}{9}
 
This question was addressed to me during an interview.
 
This intriguing question originated from Product of Two Vectors-2 topic in portion Vector Algebra of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
Interview Questions and Answers, Database Interview Questions and Answers for Freshers and Experience

1 Answers
Editor">Editor Staff answered 11 months ago

Right choice is (b) –\frac{7}{2}
 
Explanation: Given that: \vec{a}=\hat{i}-\hat{j}+3\hat{k}, \,\vec{b}=5\hat{i}-2\hat{j}+\hat{k} \,and \,\vec{c}=\hat{i}-\hat{j}
 
Also given, \vec{a}+μ\vec{b} is perpendicular to \vec{c}
 
Therefore, (\vec{a}+μ\vec{b}).\vec{c}=0
 
i.e. (\hat{i}-\hat{j}+3\hat{k}+μ(5\hat{i}-2\hat{j}+\hat{k})).(\hat{i}-\hat{j})=0
 
((1+5μ) \,\hat{i}-(1+2μ) \,\hat{j}+(μ+3) \,\hat{k}).(\hat{i}-\hat{j})=0
 
1+5μ+1+2μ=0
 
μ=-\frac{7}{2}.