True or False The following 10 problems are true or false questions, one point each. 1....

 

Transcribed Image Text:

True or False The following 10 problems are true or false questions, one point each. 1. If u and v are three-dimensional real vectors and u v = 0, then either u = 0 or v=0. 2. If u and v are three-dimensional real vectors and ux v = 0, then either u = 0 or v = 0. 3. Let u, v and w be three-dimensional real vectors, g(u, v) = uv, and h(u, v) = u x v. Then one of the differences between g and h is that g: R³ x R³ R³ while f: R³ x R³ → R. such that r" exists, then [r(t)×r' (t)] = 4. Let r be a three-dimensional real vector-valued function r"(t) x r(t). = 5. Suppose we have a function f such that f(u, v. w) three-dimensional real vectors. Then we can say that f: R³ x R³ x R³ → R. 6. The dot product is an inner product. 7. The cross product is an inner product. ||u (vx w), where u, v, and w are 8. When working over R³, the equations 2 = y and z = y, determine a surface. 9. Suppose that z = f(x, y) is a differentiable function of r and y, where a = g(s, t) and y = h(s, t) are differentiable functions of s and t. Then. = + 10. When working over R³, the equations z = 1-e-v 1+e-v and y = ln(), determine a curve. True or False The following 10 problems are true or false questions, one point each. 1. If u and v are three-dimensional real vectors and u v = 0, then either u = 0 or v=0. 2. If u and v are three-dimensional real vectors and ux v = 0, then either u = 0 or v = 0. 3. Let u, v and w be three-dimensional real vectors, g(u, v) = uv, and h(u, v) = u x v. Then one of the differences between g and h is that g: R³ x R³ R³ while f: R³ x R³ → R. such that r" exists, then [r(t)×r' (t)] = 4. Let r be a three-dimensional real vector-valued function r"(t) x r(t). = 5. Suppose we have a function f such that f(u, v. w) three-dimensional real vectors. Then we can say that f: R³ x R³ x R³ → R. 6. The dot product is an inner product. 7. The cross product is an inner product. ||u (vx w), where u, v, and w are 8. When working over R³, the equations 2 = y and z = y, determine a surface. 9. Suppose that z = f(x, y) is a differentiable function of r and y, where a = g(s, t) and y = h(s, t) are differentiable functions of s and t. Then. = + 10. When working over R³, the equations z = 1-e-v 1+e-v and y = ln(), determine a curve.

Answer rating: 100% (QA)

Answer6 The dot product i... View the full answer