2. Let x'= [5, 1, 3] and y' =[-1, 3, 1]. (a) Find the inner product, y'x. (b) Find x- - 2y. (c) Find the length of x, Lx. (d) Find the length of y, Ly.
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- Find a unit vector tangent to the curve of intersection of -x^2 - 2y^3 = z - 3 and 25/x2 - 4y - 3z^2 = - x + 6 at the point (1,1,0).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?Find two orthogonal vectors in the plane x + y + 2z = 0. Make them orthonormal.
- 2.b) Which vector is not normal at the plane defined by 2x - 4y-6z+1=0?The diagram shows a small block B, of mass 0.2kg, and a particle P, of mass 0.5kg, which are attached to the ends of a light inextensible string. The string is taut and passes over a small smooth pulley fixed at the intersection of a horizontal surface and an inclined plane.The block can move on the horizontal surface, which is rough. The particle can move on the inclined plane, which is smooth and which makes an angle of θ with the horizontal where tanθ = 3/4The system is released from rest. In the first 0.4 seconds of the motion P moves 0.3m downthe plane and B does not reach the pulley.(a) Find the tension in the string during the first 0.4 seconds of the motion.(b) Calculate the coefficient of friction between B and the horizontal surface.Find the parametrization of two different curves from the point (2,4) to (3,9). Compute the work done of the vector field F=〈2xy,x2+2〉over the two curves found in part (a).