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Solve the problem. (Give your answer as a terminating decimal.)Find x so that the vectors v = i + xj and w = -3i + 5j are orthogonal.

Solve the problem.For the triangle with vertices located at A(5, 3, 3), B(4, 5, 2), and C(1, 1, 1) , find a vector from vertex C to the midpoint of side AB.

Solve the problem.A pilot wants to fly on a bearing of N 62.7° E. By flying due east, he finds that a 55-mph wind, blowing from the south, puts him on course. Find the airspeed of the plane.

Find the corresponding position vector. Define the points P = (5, 7) and Q = (-1, 3). Find the position vector corresponding to .

Find the triple scalar product (u x v) ∙ w of the given vectors.u = -5i – 3j + 4k; v = 5i – 2j + 2k; w = 5i – 9j – 10k

Find projwv.v = -2i + 5j; w = -2i + j

Find the line of intersection between the two planes.-5x + 6y = 7    and    5y – 5z = 5

Find the line of intersection between the two planes.-2x + 2y = -2   and   -2y + 5z = 4

Write the equation for the plane.The plane through the points P(-1, 4, -23) , Q(2, 2, 2) and R(1, -6, 11)

Write the equation for the plane.The plane through the points P(-1, 3, -8) , Q(2, 3, 1) and R(1, -8, 31).