midterm1

# midterm1 - = proj n b=(c U,V 3 u.v 0(i a= u b= u v(ii a= su...

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1 Practice Problems for Mid-Term 1 (261) (1) In each situation determine whether a and b are Never, Sometimes, or Always orthogonal: Give reasons/ example, algebraic and /or geometric. (a) U and V 2 ; a = proj u (v) b= v-proj u (v) (b) U and v n ; a = proj u (v) b= v-proj u (v) (c) In 3 ; x and P are points on a plane with normal vector n. (i) = and = (ii) = and = (iii)
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Unformatted text preview: = proj n b= (c) U,V 3 u.v 0 (i) a= u b= u v (ii) a= su+tv b= u v (iii) a= su + tu v b= u s 0 (iv) a= (u.v) b= u (2) Given u and v 3 ; u and v 0 v =4 and proj u (v) =2 and u=3proj u (v). (a) What are the possible angles between u and v (b) Draw a picture that suggests the value of v-proj u (v) (c) Find u . (d) Find u.v...
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