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Question: homework 1 linear systems and differential equations due date monday...

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Homework 1- Linear Systems and Differential Equations Due Date: Monday, January 28th 2019 Instructions: To get full marks you have to show all necessary work. 1) Find a unit vector in the opposite direction of v- 7i-+4k. 2) For what value(s) of c are u- ci + 4j +3k and v 3i - 2j + 12k orthogonal? 3) Find the angle between a diagonal of a cube and one of its edges. 4) Determine whether the vectorsu (2,4,-8) and V- (5,3,7) make an acute angle, make an obtuse angle, or are orthogonal 5) Prove that ifu and v are two vectors in R, then 1 + vi,lu-vf-ziu +21y? 6) Consider the two vectors in IR2 3 and v-i+3 a) Use both graphical and analytical method to find projvu b) Use both graphical and analytical method to find projuv.

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