Q8 of 45 Page 1

If a unit vector vector a makes angles pi /3 with i , pi /4 with j and an acute angle θ with k then find the value of θ.

Given that is a unit vector

Let be the unit vector


It is given that makes an angle with



It is given that makes an angle with



It is given that makes an acute angle θ with


…(i) Now, we know that the unit vector has magnitude 1


⇒ x2 + y2 + z2 = 1










Putting the value of z in eq. (i), we get


If





If





[∵ cos(π – x) = -cos x]




But it is given that θ makes an acute angle with


So, is not possible.


Hence, the value of


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