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The unit vector in the direction of the ...

The unit vector in the direction of the sum of vectors `hat i + hat j + hat k` and `2 hat i + 3 hat j + 4 hat k` is

A

`(1)/(5sqrt2)(3 hat i + 4 hat j + 5 hat k)`

B

`(1)/(5 sqrt2)(3 hat i - 4 hat j - 5 hat k)`

C

`(1)/(2 sqrt2)(4 hat i + 3 hat j + 5 hat k)`

D

`(1)/(3sqrt2(-3 hat k + 4 hat i + 5 hat j)`

Text Solution

Verified by Experts

The correct Answer is:
A
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Knowledge Check

  • A unit vector perpendicular to the vectors veca = 2 hat i - 6 hat j - 3 hat k and vec b = 4 hat i + 3 hat j - hat k is

    A
    `(4 hat i + 3 hat j - hat k)/(sqrt 26)`
    B
    `(2 hat i - 6 hat j - 3 hat k)/(7)`
    C
    `(3 hat i - 2 hat j + 6 hat k)/(7)`
    D
    `(2hat i - 3 hat j - 6 hat k)/(7)`

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    Thescalar product of the vector hat i + hat j + hat k with a unit vector along the sum of vectors 2 hat i + 4 hat j - 5 hat k and lambda hat i + 2 hat j + 3 hat k is equal to one. Find the value of lambda .

    Find a unit vector in the direction of the vector vec a = 2 hat i + 2 hat j + hat k .

    Find the projection of the vector hat i + 3 hat j + 7 hat k on the vector 7 hat i - hat j + 8 hat k .

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    Show that the vectors 2 hat i + 3 hat j + 4 hat k and 4 hat i + 6 hat j + 8 hat k are collinear.

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