MATH 0280 Midterm: MATH 280 practiceCh4-147
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7: -3, ||~a|| = 3 and || 3~b|| = 3||~b|| = 3 4 = 6. Comment: use ||~a|| from part c); two vectors are. Comment: find ||~b|| rst (use your work from part c); the normalized vector is. Comment: use the normalized vector from part e), and stretch it by a factor of 3 (multiply each component of the vector by 3: 5 . Comment: find the cosine of the angle rst, you should get (use your answers and your work from parts b) and c) ) Any vector (with at least one non-zero coordinate), such that its dot product with ~a is equal to 0, works. 0: |~a ~b| = | 3| = 3, ||~a|| = 3 and ||~b|| = 2, so. 3 3 2 3 2 3 4, true: ~a + ~b = , ||~a + ~b|| = 1, ||~a|| = 3 and ||~b|| = 2, so. 1 3 + 2 0 3 + 1 true.
