Question

1. Let ⃗u = −2[4,0,1]+[−1,3,−2] and ⃗v = 3[4,0,1]+5[−1,3,−2]. Let w⃗ = 3⃗u−⃗v. Express w⃗ as a linear combination of the vectors [4, 0, 1] and [−1, 3, −2].

2. Let ⃗u and ⃗v be two vectors in Rn. Suppose that ||⃗u|| = 3, ||⃗u − ⃗v|| = 5, and that⃗u.⃗v = 1. What is ||⃗v||?.

3. Let ⃗u and ⃗v be two vectors in Rn. Suppose that ||⃗u|| = 5 and that ||⃗v|| = 2. Show that ||⃗u − ⃗v|| ≥ 3. (Hint: one can write ⃗u as (⃗u − ⃗v) − ⃗v).

Answer 1