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.)

Expert Solution

- p10,-3,0), 025,1,-2), R15,21) P Q = <5, 4,-2) ,PR=<5,5,1) the cross product of two hectors sites a necter orthogenal to bot

milcah answered 2 years ago

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].

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).

Show that if P;Q are projections such that R(P) = R(Q) and N(P) = N(Q), then...

Show that if P;Q are projections such that R(P) = R(Q) and N(P) = N(Q), then P = Q.

Linear Algebra we know that x ∈ R^n is a nonzero vector and C is a...

Linear Algebra we know that x ∈ R^n is a nonzero vector and C is a real number. find all values of C such that ( In − Cxx^T ) is nonsingular and find its inverse knowing that its inverse is of the same form

Prove p → (q ∨ r), q → s, r → s ⊢ p → s

(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) Find the matrix representation for the orthogonal projection Pr : R 4 → R 4...

(a) Find the matrix representation for the orthogonal projection Pr : R 4 → R 4 onto the plane P= span 1 -1 -1 1 -1 -1 1 1 (b) Find the distance of vector ~y = 2 0 0 4 from the plane P.

find the projection vector of the vector v = (2,3,5) onto the plane z = 2x...

find the projection vector of the vector v = (2,3,5) onto the plane z = 2x + 3y -1

Find the vector and parametric equations for the plane. The plane that contains the lines r1(t)...

Find the vector and parametric equations for the plane. The plane that contains the lines r1(t) = <6, 8, 8,> + t<-2, 9, 6> and r2 = <6, 8, 8> + t<5, 1, 7>.

Given the function u(p,q,r)=((p-q)/(q-r)), with p=x+y+z,q=x-y+z, and r=x+y-z, find the partial derivatives au/ax=, au/ay=, au/az=

Question