Consider the following graph. 6- (4, 4) (4, 4) (1, 2) 2 | (3. 2 3 5 2. 3. (1, 2) 3 4 5 6 -1- 5- (a) Find the component form of the vector v. (V, V2) = !! (3, 2) (1, 2) 3 4 5 67 -1 -1
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- Find the terminal point of a vector of magnitude 5 that is parallel to the vector 1, 2, 3 and whose initial point is (0, 3, −2).Suppose the pathogen is currently at location (1, 1) in antigenic space. Using a vector projection, determine the vector that specifies the velocity at which the pathogen is evolving directly away from the origin. (Hint: Your final answer will be a vector in the direction of the dashed line from the graphic and will involve k and θ)The unit vector (1,0,0) is initially on the x-axis. If it is rotated in the positive xz direction by the alpha angle and at the same time rotated in the positive xy direction by the beta angle, how is the new vector defined?
- What is the vector parametric equation L(t) for the line through the points (5,-5,0) and (0,-3,3)?Find the equation of the plane in xyz-space through the point P=(3,3,2) and perpendicular to the vector n=(−2,1,5).If vector u has initial point (3,0) and terminal point (7,-2), find the linear combination of vector u. A) 4i-2i B) -4i-2j C) 10i+2j D) 7i-2j
- 2.3(4) Determines the vector equation of the line of intersection of the plan: (shown in the image)Two particles move in space, so that at each instant the vector position of each particle, A and B, is given respectively by (image). Determine the initial position of particles A and B. Do the particles collide at any point in time? If so, determine the position in which this happens.The vector v = ⟨−1, 3⟩ and its Initial point: (4, 2). Find the terminal point.