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Vector vec(A) makes equal angles with x-...

Vector `vec(A)` makes equal angles with x-,y-,and z-axis. Find the value of its components (in terms of magnitude of `vec(A)`)

A

`A/(sqrt(3))`

B

`A/(sqrt(2))`

C

`sqrt(3)A`

D

`(sqrt(3))/A`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the components of `vec(A)` makes angles `alpha, beta and gamma` with x,y and z axis respectively then `alpha=beta=gamma`
`cos^(2)theta+cos^(2)beta+cos^(2)gamma=1`
`implies 3 cos^(2)theta=1implies cos alpha= 1/(sqrt(3))`
`:. A_(x)=A_(y)=A_(z)= A cos alpha= (A)/(sqrt(3)`
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Knowledge Check

  • Two vector vec(V)andvec(V) have equal magnitudes. If magnitude of vec(A)+vec(B) is equal to n time the magnitude of vec(A)-vec(B) , then angel to between vec(A) and vec(B) is

    A
    `cos^(-1)((n-1)/(n+1))`
    B
    `cos^(-1)((n^(2)-1)/(n^(2)+1))`
    C
    `sin^(-1)((n-1)/(n+1))`
    D
    `sin^(-1)((n^(2)-1)/(n^(2)+1))`

  • A vector having magnitude 30 unit makes equal angles with each of X,Y, and Z -axes The components of vector along each of X,Y,and Z -axes are

    A
    `10sqrt(3) ` unit
    B
    `20sqrt(3)` unit
    C
    `15sqrt(3)` unit
    D
    10 unit

  • Two vectors vec A and vec B have equal magnitudes. If magnitude of vec A-vec B is equal to (n) times the magnitude of vec A-vec B , then angle between vec A and vec B is ?

    A
    ` cos^(-1) ((n-1)/(n-1))`
    B
    ` cos^(-1) ((n^2-1)/(n^2+1))`
    C
    ` cos^(-1) ((n-1)/(n-1))`
    D
    ` cos^(-1) ((n^2-1)/(n^2+1))`
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