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Unit vector along the vector hat(i) + ha...

Unit vector along the vector `hat(i) + hat(j) + hat(k)` is

A

`(1)/(3) (hat(i) + hat(k) + hat(k))`

B

`(1)/(2) (hat(i) + hat(j) + hat(k))`

C

`(1)/(sqrt3) (hat(i) + hat(j) + hat(k))`

D

`(1)/(sqrt2) (hat(i) + hat(j) + hat(k))`

Text Solution

Verified by Experts

The correct Answer is:
C
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Write a vector of magnitude of 18 units in the direction of the vector hat(i) - 2 hat (j) - 2 hat (k) .

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Knowledge Check

  • The vector in the direction of the vector hat(i) - 2 hat(j) + 2hat(k) that has magnitude 9 units is

    A
    `hat(i) - 2 hat(j) + 2 hat(k)`
    B
    `(hat(i) - 2 hat(j) + 2 hat(k))/(3)`
    C
    `3( hat(i)- 2 hat(j) + 2 hat(k))`
    D
    `9 ( hat(i) - 2 hat(j) + 2 hat(k))`

  • The projection of the vector vec( a) = 2 hat(i) - hat(j) +hat(k) along the vector vec(b) = hat(i) + 2 hat(j)+ 2hat(k) is

    A
    2
    B
    `sqrt(6)`
    C
    `(2)/(3)`
    D
    `(1)/(3)`

  • Unit vector perpendicular to the vectors hat(i) - hat(j) and hat(i) + hat(j) is

    A
    `hat(k)`
    B
    `- hat(k)`
    C
    `(hat(i) - hat(j))/( sqrt(2))`
    D
    `(hat(i) + hat(j))/( sqrt(2))`

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