АЗ. You are given that the plane P contains both the point and the line Ls, where Q has position ...
8. The position vector r of a point P is a function of the time t and r satisfies the vector differential equation d2r dr 2k (k2 n2)r g, dr2 where k and n are constants and g is a constant vector. Solve dr a and dt this differential equation given that r v when t = 0, a and v being constant vectors Show that P moves in a plane and write down the vector equation of this plane...
Two vectors p and q are given by: p = 2i + j - K q = i - 3j + 2k Find: a) p + q b) Modulus (p + q) c) Modulus (p) + Modulus (q) d) (p) x (q)
Question 9: Plane through point and line A plane contains the point P(-1,2,3) and the line L(t), where L(t) is given by equation (2, 4t - 3,1 – 4t). Find the equation of this plane. Type in the equation of the plane with the accuracy of at least 3 significant figures for each coefficient 1 ) x + ( Dy+ ( )= / Save & Grade Save only
Q2. Consider the plane P C R3 given by the equation 2z-y+2z 7 and the point v2 (a) Show that the point p-5lies in P and calculate the distance between p and v (b) Find the point qE P that lies closest to v (c) What is the distance of v to P? (d) What is the angle between the vectors v - q and p -q? (e) Does the pythagoras theorem apply to the triangle formed by the points...
Q2. Let u and v be non-parallel vectors in Rn and define Suv (a) Does the point r lie on the straight line through q with direction vector p? (b) Does the point s lie on the straight line through q with direction vector p? (c) Prove that the vectors s and p -r are parallel. (d) Find the intersection point of the line {q+λ p | λ E R} and the line through the points u and v. Q3....
1. Let P be any point on the line: 1:= (4,8, -1)+(2,0,–4),TER. Let Q be any point on the line: 12: .X-7_1-2_2+1 -6 Find the Cartesian equation of the plane formed by all the possible midpoints of the line segment PQ.
intersects the plane Q3: Find the point where the line x x = + 2t , y = -2t, z = 1+t through P (1,1,-1). Q(2,0.2) and S (0,2,1) ?
Q2. Consider the plane P C R3 given by the equation 2z-y+2z 7 and the point v2 (a) Show that the point p-5lies in P and calculate the distance between p and v (b) Find the point qE P that lies closest to v (c) What is the distance of v to P? (d) What is the angle between the vectors v - q and p -q? (e) Does the pythagoras theorem apply to the triangle formed by the points...
1. (1 point) Find two vectors vi and v2 whose sum is (-3,0), where Vi is parallel to(-2,-4) while v2 is perpendicular to-2,-4) and Answer(s) submitted: (incorrect) 2. (1 point) Find the angle θ between the vectors a- 10i -j- 5k and b 2i+j- 21k Answer (in radians): θ Answer(s) submitted: (incorrect) 3. (1 point) Find a vector a that has the same direction as -6,5,6) but has length 3. Answer: a Answer(s) submitted: (incorrect) 4. (1 point) Suppose we...
3.1 The position vectors of the points P,Q, R and S are given, respectively: per 3e is =-ex-ey. The force vector F1 = 2Ex acts on point Q. The force vector F2 =-2 acts on point S Q F X% xp Calculate the resulting moment of the forces Fi and F2 with respect to the points P and R