Test Index

CBSE Class 12 Math 2008 Solved Paper

© examsnet.com
Question : 10 of 29
Marks: +1, -0
For what value of λ are the vectors a⃗\vec{a} = 2i^+λj^+k^\hat{2i} + \lambda \hat{j} + \hat{k} and b^\hat{b} = i^−2j^+3k^\hat{i} - \hat{2j} + \hat{3k} perpendicular to each other?
Solution:  
a⃗\vec{a} = 2i^+λj^+k^\hat{2i} + \lambda \hat{j} + \hat{k}
b^\hat{b} = i^−2j^+3k^\hat{i} - \hat{2j} + \hat{3k}
If a⃗\vec{a} and b⃗\vec{b} are perpendicular to each other, then a⃗⋅b⃗\vec{a}\cdot\vec{b} must be 0.
a⃗⋅b⃗\vec{a}\cdot\vec{b} = 2i^+λj^+k^\hat{2i} + \lambda \hat{j} + \hat{k} . i^−2j^+3k^\hat{i} - \hat{2j} + \hat{3k}
0 = 2 - 2λ + 3
2λ - 5 ⇒ λ = 52\frac{5}{2}
Thus, the value of λ is 52\frac{5}{2}
© examsnet.com
Go to Question:
Prev Question
Next Question