Find the symmetric image of P(−28,18,20) about the plane passing through Q(0,0,0) and perpendicular to the...

Find the symmetric image of P(−28,18,20) about the plane passing through Q(0,0,0) and perpendicular to the vector n=[−5,5,2].

Expert Solution

Colby Messinger answered 2 years ago

Find the intersection of the line passing through P=(-10,-6,-6) and Q(50,-18,-18) and the plane passing through...

Find the intersection of the line passing through P=(-10,-6,-6) and Q(50,-18,-18) and the plane passing through points R(-10,0,0), S(0,-6,0) and T(0,0,-6).

Find the intersection of the line passing through P=(21,21) and Q(−63,168) and the line passing through...

Find the intersection of the line passing through P=(21,21) and Q(−63,168) and the line passing through points R(21,0) and S(0,21) using vectors.

(a) Find the equation of the plane passing through the point P(0, 0, 5) and the...

(a) Find the equation of the plane passing through the point P(0, 0, 5) and the line x = 1 + t, y = 1 − t, z = 4 − 5t. (b) Find parametric equations for the line passing through point (1, 2, 3) and parallel to the line x = 2 − 3t, y = 4 + t, z = 2t.

A cable that is anchored at P (0,0,0) and passes through Q (2,8,5) supports a 100...

A cable that is anchored at P (0,0,0) and passes through Q (2,8,5) supports a 100 lb weight as shown. Express the tension T in the cable in Cartesian vector form.

A) Find the equation of the plane that passes through (2, -1,3) and is perpendicular to...

A) Find the equation of the plane that passes through (2, -1,3) and is perpendicular to the line x = 2-3t, y = 3 + t, z = 5t B) Find the equation where the planes 2x-3y + z = 5 and x + y-z = 2 intersect. C) Find the distance from the point (2,3,1) to the x + y-z = 2 plane. D) Find the angle between the planes x + y + z = 1 and x-2y...

Find a nonzero vector orthogonal to the plane through the points P, Q, and R

Consider the points below. P(0, -3,0), Q(5,1,-2), R(5, 2, 1) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (b) Find the area of the triangle PQR. (Recall the area of a triangle is one-half the area of the parallelogram.)

6) a). Find the equation of the plane through the origin and perpendicular to x+y+z =...

6) a). Find the equation of the plane through the origin and perpendicular to x+y+z = 5 and 2x+y−2z = 7 b). Let A = (−1,3,0), B = (3,2,4) and C = (1,−1,5). ( I ) Find an equation for the plane that passes through these three points. ( II ) Find the area of the triangle determined by these three points.

Find the equation of the line through the point P = (0,2,−1) that is perpendicular to...

Find the equation of the line through the point P = (0,2,−1) that is perpendicular to both ⃗v = 〈3,0,1〉 and ⃗w = 〈1,−1,2〉. v and w are vectors by the way

Show the complete and neat solution. 1. A plane through the origin is perpendicular to the...

Show the complete and neat solution. 1. A plane through the origin is perpendicular to the plane 2? − ? − ? = 5 and parallel to the line joining the points A (1, 2, 3) and (4, -1, 2). Find its equation.

Determine the general equation of a plane that passes through (-1, -2,1) and is perpendicular to...

Determine the general equation of a plane that passes through (-1, -2,1) and is perpendicular to the line that passes through point (0,2,3) and through the intersection of the x + 2y plane. -z = 0 and the line: L = (x = -2 + 5t, y = 2t, z = 4 + 3t) Graph the answer

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