For what value of λ are the vectors a^{\to} = 2i^{\^}+\lambdaj^{\^}+k^{\^} and b^{\^} = i^{\^}-2j^{\^}+3k^{\^} perpendicular to each other?

CBSE Class 12 Math 2008 Solved Paper - Question 10

Question : 10 of 29

Marks: +1, -0

For what value of λ are the vectors

a↖{→}

2i↖{\^}+λj↖{\^}+k↖{\^}

and

b↖{\^}

i↖{\^}-2j↖{\^}+3k↖{\^}

perpendicular to each other?

Solution:

a↖{→}

2i↖{\^}+λj↖{\^}+k↖{\^}

b↖{\^}

i↖{\^}-2j↖{\^}+3k↖{\^}

a↖{→}

and

b↖{→}

are perpendicular to each other, then

a↖{→}.b↖{→}

must be 0.

a↖{→}.b↖{→}

2i↖{\^}+λj↖{\^}+k↖{\^}

i↖{\^}-2j↖{\^}+3k↖{\^}

0 = 2 - 2λ + 3
2λ - 5 ⇒ λ =

5/2

Thus, the value of λ is

5/2

Go to Question:

Prev Question

Next Question