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2331_hw1_key

# 2331_hw1_key - Homework is graded out of 50 points Math...

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1 Math 2331- HW 1 Key Problem: If ° = ± 1 3 5 ² , ³ = ± 1 1 1 ² , ´ = ± 1 1 −2 ² µ = ± 1 0 0 ² , ¶ = ± 0 1 0 ² , · = ± 0 0 1 ² a) ° ∙ µ = ¸. ¸ + ¹. º + ». º = ¸ b) ° ∙ ³ = ¸. ¸ + ¹. ¸ + ». ¸ = ¼ c) Express ° and ´ as a linear combination of µ, ¶ and · : ° = ¸µ + ¹¶ + »· ´ = ¸µ + ¸¶ − ½· d) Length of ° = √¸ ½ + ¹ ½ + » ½ = √¹» . e) Length of ° + ½´ = √¹ ½ + » ½ + ¸ ½ = √¹» since 3 2 5 1 v u     + =       . f) What is the cosine of the angle between ° and ³ ? Are they perpendicular? 9 3 105 cos( ) 35 35 3 v w v w θ = = = i No, not perpendicular since cos( ) 0 θ . g) Use given vectors to fill in: __ i ___ and __ j ___ are perpendicular to each other. __ i ___ and __ k ___ are perpendicular to each other. __ j ___ and __ k ___ are perpendicular to each other. ___ u __ and __ w ___ are perpendicular to each other. h) Give a vector that is perpendicular to ° . 3 0 1 , 5 ,... 0 3 -         -   i) Give a vector that is perpendicular to ° + ³ .

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2331_hw1_key - Homework is graded out of 50 points Math...

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