Consider the following vectors in V = R³ over F = R. v₁ = (1,0,1) U2 = (0,1,2) √3 = (1,2,0)

Q: (3) Suppose a vector x is orthogonal to vectors u and v. Show that x is orthogonal to u+v.

A: We will use the fact that x is orthogonal to u and v to prove that x is orthogonal to u+v also

Q: 1 u=-----(1, 1, 1, 0), V 3 1 -- (-1,-1, 2, 0) W = V6 1 =(1,-1, 0, 0) V 2

A: Here we have to determine whether or not the following set of vectors { u, v, w } are both…

Q: u = (2, 3,-1) v= (0, 1, -2) w = (2, 4, -3).

A:

Q: The normal vector to the vectors u = (2, 1, 1) and v = (1, -1, 3) is:    4i - 5j + 3k  4i - 5j -…

A:

Q: Let ū = (4, –2), ū = (-2,0), and w = (2, 2). Find the vector x that satisfies Tu – u +x = 5x + w. In…

A: Given Let Plugging the values in the equation:

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

A:

Q: Find a unit vector orthogonal to both u and v. u = 2i5j + 3k 2-3 V = + -k 10

A:

Q: O Are vectors v1 = ---- 2,₂ -17 3 linearly independent? Show work.

A: The given vectors are .If  are linearly independent .Then Where a, b and c are constant.

Q: Let u = (2, 1, -2), v= (0,3,-5), and w = Compute the indicated vectors. (a) u × v = (?, ?, ?) (b) -…

A:

Q: b) u = (3, -1), v = (1, 5) et w = (8, -2) c) i = (1, 0, 0), j = (0, 1, 0) et k = (0, 0, 1) gajte…

A:

Q: For the vectors à = (1, 0, −4) and ¯` = (5, 2, 1) what is the scalar a projection of onto a 1/17 √17…

A: The vectors are given by÷

Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

A:

Q: Write an equation for the function graphed below 15+ 14+ 13+ 12+ + + + -7 -6 -5 -4 -3 -2 -1 -1 -2 -3…

A: A following graph:To Find:Equation of the above graph.