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Step-by-step Answer
PAGE: 609SET: ExercisesPROBLEM: 7
Please look in your text book for this problem Statement

a)

The vectors are and .

Dot product definition:

.

(b)

Find the angle between and .

Cosine of the angle between two vectors: .

Find magnitude of vector : .

.

.

Find magnitude of vector : .

.

.

Apply formula: .

italic cos italic theta equal fraction numerator 0 over denominator square root of 2 square root of 2 end fraction.

italic cos italic theta equal 0 over 2 equal 0.

italic theta equal italic cos to the power of minus 1 end exponent open parentheses 0 close parentheses.

italic cos to the power of minus 1 end exponent open parentheses italic cos 90 degree close parentheses equal 90 degree

italic theta equal 90 degree.

c)

Dot product of the vectors , so the vectors are orthogonal.

The vectors are orthogonal.

a) .

b) The angle italic theta equal 90 degree.

c) The vectors are orthogonal.



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