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check Wether the vector ((hati)/sqrt (2)...

check Wether the vector `((hati)/sqrt (2)+(hatj)/sqrt(2))` is a unit vector or not .

A

YES

B

NO

C

Cannot be determined

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
A
Aunit vector is a vector with magnitude 1.
The magnitude of given vector is
`|(hati)/(sqrt(2)) +(hati)/(sqrt(2))|=sqrt (((1)/(sqrt(2)))^(2)+((1)/(sqrt(2)))^(2))=sqrt ((1)/(2)+(1)/(2))=sqrt(1)=1`
As magnitude of given vector is 1.
`therefore `It is a unit vector.
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Knowledge Check

  • The angle between the Z-axis and the vector (hati+hatj+sqrt(2)hatk) is

    A
    `30^(@)`
    B
    `45^(@)`
    C
    `60^(@)`
    D
    `90^(@)`

  • What is the interior acute angle of the parallelogram whose sides are represented by the vectors (1)/(sqrt2) hati + (1)/(sqrt2) hatj + hatk and (1)/(sqrt2) hati - (1)/(sqrt2) hatj +hatk ?

    A
    `60^@`
    B
    `45^@`
    C
    `30^@`
    D
    `15^@`

  • You are given a vector, vec P =(1)/(sqrt(2)) cos theta hati+(1)/(sqrt(2)) sin theta hatj What is the unit vector in the direction of vec P ?

    A
    `(1)/(sqrt(2)) [cos theta hati+sin theta hatj]`
    B
    `cos theta hati+ sin theta hatj`
    C
    `cos theta hati- sin theta hatj`
    D
    `(1)/(2) [cos theta hati- sin theta hatj]`

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    If the magnitude of the vector product of the vector hati+hatj+hatk with a unit vector along the sum of vector 2hati+4hatj-5hatk and lambda hati+2hatj+3hatk is equal to sqrt2 , then find the value of 'lambda'

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