# Vector problem

## 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

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

• Yodaa
SteamKing
Staff Emeritus
Science Advisor
Homework Helper

## 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

• Yodaa
oh i had completely misinterpreted the question! Thanks for the help @Yosty22

• Yosty22
I got the answer after reading up about direction cosines! Thanks for the help @SteamKing