2A-3(B-C)= ΟΙ ΑΣΦ ? In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors A = (1,0, -3), B = (-2, 5, 1), and C = (3,1,1). Calculate the following, and express your answers as ordered triplets of values separated by commas.

If , and , find the unknown constants a and b such that .

Figure 1.19 shows two vectors lying in the xy-plane. Determine the signs of the x- and y-components of A, B, and A+B.

A skater glides along a circular path of radius 5.00 m in clockwise direction. ‘When he coasts around one- half of the circle, starting from the west point, find (a) the magnitude of his displacement vector and (b) how far he actually skated. (c) What is the magnitude of his displacement vector when he skates all the way around the circle and comes back to the west point?

Assuming the +x -axis is horizontal and points to the tight, resolve the vectors given In the following figure to their scalar components and express them in vector component form.

A trapper walks a 5.0-lan straight-line distance from her cabin to the lake, as shown in the following figure. Determine the east and north components of her displacement vector. How many more kilometers would she have to walk if she walked along the component displacements? What is her displacement vector?

Find the components of the acceleration vector a in spherical coordinates.

Show that (2arr+2brr)dt=ar2+br2+const. where r is the vector from the origin to the point (x1, x2, x3). The quantities r and r are the magnitudes of the vectors r and r, respectively, and a and b are constants.

Vectors A and B are two orthogonal vectors in the xy -plane and they have identical magnitudes. If A=3.0 i+4.0 j , find B .

Consider the three displacement vectors A=(3i3j)m, B=(i4j)m, and C=(2i+5j)m. Use the component method to determine (a) the magnitude and direction of the vector D=A+B+C and (b) the magnitude and direction of E=AB+C.