H.W. : Find the Transformation matrix that transform vectors from cartesian unit vectors to the cylindrical unit vecotrs.

Q: Find the scalar and vector projection of the vector b = (−1, −1, 1) onto the ve Scalar projection…

A: Scalar Projection :  The length of the projection is called scalar projection. Vector Projection :…

Q: Find the parallel projection of the vector v = onto the vector w=.

A: Given problem:- Find the parallel projection of the vector v=<4, -5, 7> onto the vector…

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

A:

Q: Find the position vector v that corresponds to the vector graphed below. Note that each box in the…

A: Given the query is find the component form of vector.

Q: What is the definition of the triple scalar product for vectors u, v, and w in ℝ3?

A: To Define: Scalar Triple Product for vectors u, v and w in ℝ3.

Q: Find a vector equation and a parametric equation for the line that passes through the point (5, 1,…

A: We have to solve given problem:

Q: Find the orthogonal projection of the vector onto the vector .

A:

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: (a) AB-BC (b) projABAC (the vector projection of AC onto AB) (c) the area of AABC

A:

Q: Find the projection of the vector v onto the vector w if v = 2i + j and w = 6i + 3j

A: we have given v and w vectors . We have to find the projection of the vector v onto the vector w

Q: Find a unit vector perpendicular to i-j and to i +k and with a positive k component.

A:

Q: Find a unit vector in the direction of vector v = ⟨−2, 3⟩

A:

Q: Vector i = (- 2, – 6, 4) has initial point (6, 8, – 5). Find the terminal point.

A: