Consider the following. u = 6i – j - k, v = -i + 5j + 3k | (a) Find the projection of u onto v. (b) Find the vector component of u orthogonal to v.

Q: Consider the following. u = 9i + 4j, v = 8i + 2j (a) Find the projection of u onto v. (b) Find the…

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Q: Find a unit vector orthogonal to both u and v. u = -5i – 3j - 2k | V =

A: Two vectors A and B are said to be orthogonal to each other if and only if their dot product is zero…

Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

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Q: Calculate the triple scalar products w. (vx u) and u (w x v), where u = (7, 2, -1), v = (2, 8, -3),…

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Q: Consider the vector v = (x, 2) in R2. If you rotate the vector by 90-degrees counter-clockwise, then…

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Q: nd the unit vector 3i - 4j+ 5k perpendicular to the vectors: 4i + 5j-6k

A: Let the given vectors be  u→=3i-4j+5kv→=4i+5j-6k we have to find the unit vector perpendicular to…

Q: Define irrotational vector. Is the vector A =(6xy+z³)i+(3x² - 2)j+(3xz² – y)k irrotational? Justify…

A: we have the vector A=(6xy+z3)i+(3x2-z)j+(3xz2-y)k we have to check weather the given vector is…

Q: Find an equation for the plane that passes through the point (3, -2, 1) normal to the vector n = 2i…

A: Given:A point (3, -2, 1) normal to the vector n = 2i + j + kThe normal vector can be written as,

Q: Make all obvious simplifications.

A: We have to solve

Q: Consider the following. u = -9i – 2j - 4k, v = 4j + 4k (a) Find the projection of u onto v. (b) Find…

A: Explanation of the answer is as follows

Q: In R, evaluate the alternating 2-form 5 = -3 · dx A dy on the pair of vectors (a, b) if a = (4, 2,…

A: In ℝ3, we have to evaluate the alternating 2-form ξ=-3·dx∧dy on the pair of vectors (a,b). a=4,2,12…

Q: Find the equation of the plane with normal vector n = (8, 7, 3) passing through the point (4,,9) in…

A: Use equation of plane and put value

Q: Consider the following. u = -9i – 4j – 2k, v = 4j + 4k (a) Find the projection of u onto v. (b) Find…

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