A displacement vectorr→in the xy plane is 89 m long and directed at angle θ = 23° in the figure. Determine (a) the x component and (b) the y component of the vector.

If A + B = 0, the corresponding components of the two vectors Aand Bmust be (a) equal, (b) positive, (c) negative, (d) of opposite sign.

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.

Vector B is 5.0 cm long and vector A is 4.0 cm long. Find the angle between these two vectors when |A+B|=3.0cm and |AB|=3.0cm .

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.

At one point in space, the direction of the electric field vector Is given In the Cartesian system by the unit vector . If the magnitude of the electric field vector is E=400.0V/m , what are the scalar components , and of the electric field vector at this point? What is the direction angle of the electric field vector at this point?

For the two vectors find A − B and |A – B| component of B along A angle between A and B A × B (A − B) × (A + B)

Find the angles that vector makes with the and axes.

For what values of a are the vectors A = 2ai − 2j + ak and B = ai + 2aj + 2k perpendicular?

X is an unknown vector satisfying the following relations involving the known vectors A and B and the scalar ϕ, A × X = B, A · X = ϕ. Express X in terms of A, B, ϕ, and the magnitude of A.