ISC (Commerce) Class 12CISCE
Share

# Find Lambda If the Scalar Projection of Vec a = Lambda Hat I + Hat J + 4 Hat K on Vec B = 2hati + 6hatj + 3hatk is 4 Units - ISC (Commerce) Class 12 - Mathematics

ConceptProduct of Two Vectors Scalar (Or Dot) Product of Two Vectors

#### Question

Find lambda if the scalar projection of vec a = lambda hat i + hat j + 4 hat k on vec b = 2hati + 6hatj + 3hatk is 4 units

#### Solution

Projection of vec a on vec b is (vec a . vec b)/|vecb| = 4

= ((lambdahati + hatj + 4hatk).(2hati+6hatj + 3hatk))/(sqrt(2^2 + 6^2 + 3^2)) = 4

:. (2lambda + 6(1) + 4(3))/sqrt49  = 4

:. (2lambda + 18)/7  = 4

:. 2lambda = 28 - 18

:. 2lambda = 10

lambda = 5

Is there an error in this question or solution?

#### Video TutorialsVIEW ALL [2]

Solution Find Lambda If the Scalar Projection of Vec a = Lambda Hat I + Hat J + 4 Hat K on Vec B = 2hati + 6hatj + 3hatk is 4 Units Concept: Product of Two Vectors - Scalar (Or Dot) Product of Two Vectors.
S