Angles Formed by Vector î + ĵ + √2k̂

AI Thread Summary
The discussion focuses on determining the angles that the vector î + ĵ + √2k̂ makes with the x, y, and z axes. Initially, there was confusion regarding the interpretation of the question, with an incorrect assumption that the angles would be 90 degrees. The correct angles, as clarified by participants, are 60 degrees with the x and y axes, and 45 degrees with the z axis. The solution involves calculating the direction cosines of the vector, which led to a better understanding of the problem. The participants express gratitude for the clarification and assistance provided.
Yodaa
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Homework Statement


the angles which[/B] î + ĵ + √2k̂ makes with x axis, y-axis and z axis are?

The Attempt at a Solution


the question is basically asking us what angle î + ĵ + √2k̂ makes with î + ĵ + k̂ right?
So since √2 is just the magnitude i thought the answer would be 90, 90, 90
the answer given is 60, 60 and 45

PS: i just started learning vectors
 
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î + ĵ + √2k̂ is a vector made up of three components, but it corresponds to a single vector. From my interpretation of the question, I would assume the question expects three answers (which is seems like it does). Rather than finding the angle î + ĵ + √2k̂ makes with î + ĵ + k̂ you are finding:
a). The angle î + ĵ + √2k̂ makes with î
b). The angle î + ĵ + √2k̂ makes with ĵ
c). The angle î + ĵ + √2k̂ makes with
 
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Yodaa said:

Homework Statement


the angles which[/B] î + ĵ + √2k̂ makes with x axis, y-axis and z axis are?

The Attempt at a Solution


the question is basically asking us what angle î + ĵ + √2k̂ makes with î + ĵ + k̂ right?
So since √2 is just the magnitude i thought the answer would be 90, 90, 90
the answer given is 60, 60 and 45

PS: i just started learning vectors
##\sqrt{2}## is the coefficient of the unit vector k.

To calculate the magnitude of the vector ##i + j + \sqrt{2} k##, you still have to do some further calculations.

What you are looking for are the direction cosines of this vector:

https://en.wikipedia.org/wiki/Direction_cosine
 
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oh i had completely misinterpreted the question! Thanks for the help @Yosty22
 
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I got the answer after reading up about direction cosines! Thanks for the help @SteamKing
 
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