What is the Angle of a Vector with x, y, and z Axes?

[Leelakrishna23]

Homework Statement

If a vector makes 45 degrees and 60 degrees with x-axis and y-axis respectively then the angle it makes with z-axis is equal to

Homework Equations

The Attempt at a Solution

 

[Suraj M]

It would easier to help you if you give it a try first
You must give an attempt only then can we help you.

 

[Leelakrishna23]

I've applied the concept of direction cosines to solve it but I couldn't get the answer.

 

[Suraj M]

Welcome to PF
I didn't know you were new around
Please go through this
https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/
You must provide your working so that we can help you out further
I hope you understand

 

[Leelakrishna23]

 

[haruspex]

View attachment 94754

That looks like an answer. Do you think it is wrong?

 

[Leelakrishna23]

Actually the answer(60 degrees) is not given in the answer column. So I just wanted to know if it's correct.

 

[Leelakrishna23]

And i didn't get the cos^2 alpha + cos^2 beta + cos^2 gama=1. Can you please explain me?

 

[Suraj M]

And i didn't get the cos^2 alpha + cos^2 beta + cos^2 gama=1. Can you please explain me?

You do get 1!
The answer of 60 degrees looks fine to me.

 

[haruspex]

And i didn't get the cos^2 alpha + cos^2 beta + cos^2 gama=1. Can you please explain me?

It's just Pythagoras' formula. If a unit vector from the origin makes those angles with the axes, then the cosines are the x, y, z coordinates.

 

[Leelakrishna23]

Much appreciated, thank you.