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).
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 slope of the line PQ. P(5, -4); Q(-5,2)
the plane PQ X PR 1. Find unit vector the perpendicular to P(1,1,1), Q(2,1,3), R(2, 2, 1).
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
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.
+4 +Q a. Find the electric Field vector E at point P (0, +a). (Calculate the magnitude, and draw b. c. d. the vector in the picture.) Sketch the electric field lines. Find the electric Field E at (x, 0) for x >a Find out the location (x, y) where the electric Field E becomes zero. (Hint: Use the solution of e).
Consider the points: P (-1,0, -1), Q (0,1,1), and R(-1,-1,0). 1.) Compute PQ and PR. 2.) Using the vectors computed above, find the equation of the plane containing the points P, Q, and R. Write it in standard form. 3.) Find the angle between the plane you just computed, and the plane given by: 2+y+z=122 Leave your answer in the form of an inverse trigonometric function.
Find the midpoint of the line segment PQ. P(9,-2); Q(-5, -2) (x, y) =
Let S denote the sphere x2 y2 2 = 1. Given two points P(1,0,0), (a) Find the distance between P and Q. Lets call this Euclidean distance. (b) Find the plane that goes through O, P, Q. What is the intersection of this plane with the sphere? (Hint: use OP × OQ as the the normal vector) (c) Observe that the length of the arc PQ is 0 the angle between OP,0Q in radians. (Hint: You know how to find...