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What is the angle between hati+hatj and ...

What is the angle between `hati+hatj and hati` ?

A

`15^(@)`

B

`30^(@)`

C

`45^(@)`

D

`60^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
The angle between two vectors `vec A and vec B` is calculated by using,
`cos theta =(vec A cdot vec B)/(AB) hati, hatj and hatk` are unit vectors
`therefore cos theta =((hati+hatj) cdot hati)/(sqrt(1^(2)+1^(2))sqrt1^(2))`
`therefore cos theta =(1)/(sqrt(2)xx sqrt(1))=(1)/(sqrt(2))`
`therefore theta =45^(@)`
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Knowledge Check

  • What is the angle between hati+hatj+hatk and hatj ?

    A
    `(pi)/(6)`
    B
    `(pi)/(4)`
    C
    `(pi)/(3)`
    D
    none of these

  • Assertion: Angle between hati+hatj and hati is 45^(@) . Reason: hati+hatj is equally inclined to both hati and hatj and the angle between hati and hatj is 90^(@) .

    A
    If both assetion and reason are true and the reason is the correct explanation of the assertion.
    B
    If both assertion and reason are true but reason is not the correct explanation of the assertion
    C
    If assertion is true but reason is false
    D
    If the assertion and reason both are false.

  • What is the angle between vecA = 5hati - 5hatj and vecB = 5hati-5hatj ?

    A
    `90^@`
    B
    `45^@`
    C
    `0^@`
    D
    `60^@`

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