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the angle between the vectors (hati+hatj...

the angle between the vectors `(hati+hatj)` and `(hatj+hatk)` is

A

`45^(@)`

B

`90^(@)`

C

`-45^(@)`

D

`180^(@)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given `A=hati+hatj`
`B=hati-hatj`
We know that `A.B=|A||B|costheta`
`rArr (hati+hatj).(hati-hatj)=(sqrt(1+1))(sqrt(1-1))cos theta`
Where `theta` is the angle between `A` and `B`
`rArr cos theta=(1-0+0-1)/(sqrt2sqrt2)=0/2=0`
`rArr theta=90^(@)`
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Assertion : The angle between the two vectors (hati + hatj) and (hatj + hatk) is (pi)/(3) radian. Reason : Angle between two vectors vecA and vecB is given by theta = cos^(-1)((vecA*vecB)/( AB))

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Knowledge Check

  • Assertion: The angle between the two vectors (hati+hatj) and (hatj_hatk) is (pi)/(3) radian. Reason: Angle between two vectors vecA and vecB is given by theta=cos^(-1)((vecA.vecB)/(AB))

    A
    If both Assertion `&` Reason are True `&` the Reason is a correct explanation of the Assertion.
    B
    If both Assertion `&` Reason are True but Reason is not a correct explanation of the Assertion.
    C
    If Assertion is True but the Reason is False.
    D
    If both Assertion `&` Reason are false.

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    `(pi)/(4)`
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    D
    None of these

  • The angle between vectors (hati+hatj) and (hatj+hatk) is :

    A
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