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If vec A =2 hat I -5 hat k, find (i) | v...

If `vec A =2 hat I -5 hat k`, find (i) | vec A| and (ii) the direction cositnes of the vector `vec A`.

A

`cos alpha = A_(x) /A =2/(sqrt45), cos beta =A_(y)/A =4/sqrt 45) and cos `gamma =A_(z)/A =(-5)/(sqrt4)

B

`cos alpha = A_(x) /A =2/(sqrt2), cos beta =A_(y)/A =4/sqrt 45) and cos `gamma =A_(z)/A =(-5)/(sqrt45)

C

`cos alpha = A_(x) /A =2/(sqrt45), cos beta =A_(y)/A =4/sqrt 45) and cos `gamma =A_(z)/A =(-5)/(sqrt45)`

D

`cos alpha = A_(x) /A =2/(sqrt45), cos beta =A_(y)/A =4/sqrt 45) and cos `gamma =_(z)/A =(-5)/(sqrt45)

Text Solution

Verified by Experts

The correct Answer is:
C
(i) `A= sqrt (A_(x)^(2) +A_(y)^(2) +A_(z)^(2)) =sqrt((2)^(2) +(4) ^(2) + (-5)^(2)) =sqrt45`
(ii) `cos alpha = A_(x) /A =2/(sqrt45), cos beta =A_(y)/A =4/sqrt 45) and cos `gamma =A_(z)/A =(-5)/(sqrt45)`.
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