Tamil Nadu Board of Secondary EducationHSC Arts Class 11th

# Find the value of λ for which the vectors aijka→=3i^+2j^+9k^ and bijkb^=i^+λj^+3k^ are parallel - Mathematics

Sum

Find the value of λ for which the vectors vec"a" = 3hat"i" + 2hat"j" + 9hat"k" and hat"b" = hat"i" + lambdahat"j" + 3hat"k" are parallel

#### Solution

Given that the vectors vec"a" = 3hat"i" + 2hat"j" + 9hat"k" and hat"b" = hat"i" + lambdahat"j" + 3hat"k" are parallel.

∴ vec"a"  = "m"vec"b"

The condition forthe two vectors vec"a" and vec"b" to be parallel is vec"a" = lambda vec"b"

3hat"i" + 2hat"j" + 9hat"k" = "m"(hat"i" + lambdahat"j" + 3hat"k")

3hat"i" + 2hat"j" + 9hat"k" = "m"hat"i" + "m"lambdahat"j" + 3"m"hat"k"

(3 - "m")hat"i" + (2 - lambda"m")hat"j" + (9 - 3"m")hat"k" = 0

∴ 3 - "m" = 0, 2 - lambda"m" = 0, 9 - 3"m" = 0

m = 3, 2 = lambda"m"

2 = lambda xx 3

⇒ lambda = 2/3

∴ Required value of lambda is 2/3.

Concept: Representation of a Vector and Types of Vectors
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