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Given vec(A) = 3hat(i) + 2hat(j) and vec...

Given `vec(A) = 3hat(i) + 2hat(j) and vec(B) = hat(i) + hat(j).` The component of vector `vec(A)` along vector `vec(B)` is

A

`1/sqrt2`

B

`3/sqrt2`

C

`5/sqrt2`

D

`7/sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
C
`vecA.vecB=|vecA||vecB|cos theta" or " cos theta=(vecAvecB)/(|vecA||vecB|)`
The componemt of `vecA` in the direction of `vecB`
`=|vecA|cos theta=|vecA|(vecA.vecB)/(|vecA||vecB|)=(2+3)/sqrt3=5/sqrt2`
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Knowledge Check

  • vec(A) and vec(B) are two vectors given by vec(A)=2hat(i)+3hat(j) and vec(B)=hat(i)+hat(j). The magnitude of the component of vec(A) along vec(B) is

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    11
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