in the direction of the vector OR. Put your answer in the Given the points P...
Q = (0,6, -4) R= (5,-4, -5) Consider the triangle with vertices: P= (-2,0, -1) (a) Find the vectors PO, PŘ, and QŘ (b) What is the measure of the angle at P (ZQPR)? (c) What is the perimeter of the triangle APQR ? (d) What is the area of the triangle APQR? (e) Find a vector that is perpendicular to the plane containing P, Q, and R Verify that the vector you have found is perpendicular to PO (f)...
Moving to another question will save this response. Question 15 Q14B Given the plane P which contains the points A(3, 2, -4), B(5, 2, 1) and C(2, -3, -4). Note: Write your answers in the vector form of ai + bj + ck. a) Find the position vector AB. АВ: b) Find the position vector AC. AC = c) Find AB X AC. AB x AC = Asus AB x AC = d) Determine the parametric equations for the line...
[7 points) Given the point A(1,2,1) and the vector v = (2,1,5): (a) Find the point B such that AB V. (b) Find the unit vector u in the opposite direction of v. (c) Find a vector equation for the line L which passes through A and is parallel to v. (d) True or False?: The line L is a subspace of R3. Give a brief explanation of your answer. (e) Find a general equation of the plane P that...
Let P(0,1,0), Q(2,1,3), R(1,-1,2). (la) Compute PQxPR. (1b) Find the equation of the plane through P, Q and R in the form ax+by+cz=d (10) What is the angle formed by this plane and the xy-plane? Please answer ic.
(1) Equation of a Plane Let P(1,1,-1), Q(1,2,0), R(-2,2,2). (la) Compute PQxPR. (1b) Find the equation of the plane through P, Q and R in the form ax+by+cz=d. (10) What is the angle formed by this plane and the xy-plane?
Find the general equation and a vector equation of the plane that passes through the points p(1,2,4) Q(1,-1,6) R(1,4,8)
(1 point) Find the points on the surface 3x2 + 4y2 3z2 -1 at which the tangent plane is parallel to the plane ) and We were unable to transcribe this imageWe were unable to transcribe this image(1 point) Consider the surface xuz48 A. Find the unit normal vector to the surface at the point (3, 4,4) with positive first coordinate. B. Find the equation of the tangent plane to the surface at the given point. Express your answer in...
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.
(a) Find a unit vector that is orthogonal to the plane through the points P(0,0,–3), Q(4,2,0), and R(3,3,1) (b) Find two non-parallel vectors that are orthogonal to the vector Ŭ = i + 2) + 3k (c) Find the angel between the vector Ở = 51 + 21 – k and the z - axis (d) Describe why it is impossible for a vector to have the following direction angles 511 6 -, B = 3, and y TT π...
The velocity vector of an object is given by y(t) = (* sin(at), 1, a cos(at)). Assume that at t = 1, the object is at the point P(1,1,0). (a) Find the position vector F(t) of the object. (b) Find parametric equations of the line which is tangent to r(t) at P. (c) Find the distance that the object traveled from the point t = 0 to t = 1. (d) Find an equation for the normal plane of r(t)...