linear algebra homework

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Mathematics

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I have uploaded 5 questions on word file for you.

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This homework covers the following measurable student objectives: • Determine the inner product of two vectors, the length of a vector in an inner product space, and the cosine of the angle between two vectors. • Determine the cross product of two vectors in 3-space 1.Find the cosine of the angle between the following pairs of vectors and state whether the angle is acute, obtuse or 90 degrees. A. u = (3, 3, 3), v = (1, 0, 4) B. u = (6, 1, 4), v = (2, 0, -3) C. u = (2, 4, -8), v = (5, 3, 7) 2. Find the area of the parallelogram determined by the vectors u and v. A. u = (1, -1, 2), v = (0, 3, 1) B. u = (2, 3, 0), v = (-1, 2, -2) 3. Find the area of the triangle in 3-space that has the given vertices. P1(2, 6, -1), P2(1, 1, 1), P3(4, 6, 2) 4. Use the cross product to find the sine of the angle between the vectors u = (2, 3, -6) and v = (2, 3, 6) 5. Let v = (1, 0, 2, 1, 3). Find the norm of v, a unit vector that has the same direction as v, and a unit vector that is oppositely directed to v
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