Carefully draw the line segment PQ that connects P=(4, 5, -3) and Q=(0, -4, 2) . Include dotted vertical lines from the xy-plane to P and Q to show perspective. Find the distance between P and Q, from the previous problem. Then find the coordinates of the midpoint of the line segment PQ . Let u= -3i+5j+7k and v= 10i+j-2k . Show that u × v is orthogonal to the vector v .
Find the midpoint of the line segment PQ. P(9,-2); Q(-5, -2) (x, y) =
Fourth Homework (1) Let P-(**.0) and Q ( . (a) Find the pole of the line PQ (b) Find the parametrization of the line PQ (c) Does (ch,顽週lie on the line PQ? 克,2 7, ) lie on the line PQ? (2) Find the distance between the lines (1,0,-1) + t(2,3,0) and m (2,-1,3) +s(0, 1,2). (3) Let A and B be two distinct points of S2. Show that X e I d(X, A) = d(X, b)) is a line and...
If P (3, 1) and Q (-3, -7), find The distance PQ Enter If P (3, 1) and Q (-3, -7), find The distance PQ Enter
Find the three angles of the triangle with the given vertices: P(1,1,1), Q(1,−5,2), and R(−2,2,6) Find a nonzero vector orthogonal to the plane through the points: A=(0,1,−1), B=(0,6,−5), C=(4,−3,−4)
Find the standard representation of the vector ??PQand then find ‖??‖‖PQ‖ given ?(3,0,−4)P(3,0,−4) and ?(0,−4,3)Q(0,−4,3).
Let P and Q be two projectors, such that PQ zQP prove that (PQ) is a projector and (a) CLPQ) = c(p). ndo) (6) Null (PQ) = Null P + Null Q
Find the volume of the parallelopiped with adjacent edges PQ, PR, PS where P(-5, 3, 5), Q(-3, 6, 8), R(-6, 2, 4), S(1, 1, 7).
Consider the points P(0,0,9) and Q(-3,3,0). a. Find PQ and state your answer in two forms: (a,b,c) and ai + bj + ck. b. Find the magnitude of PQ. c. Find two unit vectors parallel to PQ.
y 1/(1-x) 5. The point P(2,-1) lies on the curve C If Q is the point (x,1/(1-x), use your calculator to find the slope of the secant line PQ a. (correct to six decimal places) for the following values of x: 1.5 (ii) 1.9 (i) 1.99 (iv) 1.999 (v) 2.5 (vi) 2.1 (vii) 2.01 (vii) 2.001 Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(2,-1) i. b. Using...