Find all the unit vectors in R4 that make an angle of /3 with (1, 1, 1, 1) and an angle

Chapter 1, Problem 12

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QUESTION:

Find all the unit vectors in R4 that make an angle of /3 with (1, 1, 1, 1) and an angle of /4 with both (1, 1, 0, 0) and (1, 0, 0, 1). _

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QUESTION:

Find all the unit vectors in R4 that make an angle of /3 with (1, 1, 1, 1) and an angle of /4 with both (1, 1, 0, 0) and (1, 0, 0, 1). _

ANSWER:

Problem 12

Find all the unit vectors in  that make an angle of  with (1, 1, 1, 1) and an angle of  with both (1, 1, 0, 0) and (1, 0, 0, 1).

                                                            Step-by-step solution

Step 1 of 3

 be the unit vector that makes an angle 0f  with

And angle  with  and

 

And

By dot product rule,

....(1)

Also

.....(2)

.....(3)

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