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Vector problem

  • #1
9
1

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
 
Last edited:

Answers and Replies

  • #2
185
4
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
 
  • #3
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
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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
##\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
 
  • #4
9
1
oh i had completely misinterpreted the question! Thanks for the help @Yosty22
 
  • #5
9
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I got the answer after reading up about direction cosines! Thanks for the help @SteamKing
 

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