The angles which a unit vector I+ j+ sqaure root 2k makes with X Y & Z respectively are a).60 , 60 , 60 b). 45 , 45 ,45 c). 60 , 60 , 45 d). 45 ,45 , 60
Answer (1)
10th Jan, 2021
Dear student,
Let the angle made by X axis be alpha
Let the angle made by Y axis be beta
Let the angle made by Z axis be gamma
Let the vector be A vector = i + j + ((2)^1/2)k
Now |A vector| = {1^2 + 1^2 + ((2)^1/2)^2}^1/2
And therefore magnitude of A vector = (4)^1/2 =2
Therefore unit vector A = i/2 + j/2 + {(2)^1/2k}/2
And therefore angle with X axis :-
cos( alpha ) = 1/2
So, alpha = 60 degrees
Therefore angle with Y axis :-
cos ( beta ) = 1/2
So, beta = 60 degrees
Therefore angle with Z axis :-
cos ( gamma ) = 1/(2)^1/2
So, gamma = 45 degrees.
So, the angle is ( 60, 60, 45 ).
This, option C is correct.
Let the angle made by X axis be alpha
Let the angle made by Y axis be beta
Let the angle made by Z axis be gamma
Let the vector be A vector = i + j + ((2)^1/2)k
Now |A vector| = {1^2 + 1^2 + ((2)^1/2)^2}^1/2
And therefore magnitude of A vector = (4)^1/2 =2
Therefore unit vector A = i/2 + j/2 + {(2)^1/2k}/2
And therefore angle with X axis :-
cos( alpha ) = 1/2
So, alpha = 60 degrees
Therefore angle with Y axis :-
cos ( beta ) = 1/2
So, beta = 60 degrees
Therefore angle with Z axis :-
cos ( gamma ) = 1/(2)^1/2
So, gamma = 45 degrees.
So, the angle is ( 60, 60, 45 ).
This, option C is correct.
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