Determine the two unit vectors that are orthogonal to i = (1,2). Which two unit vectors are parallel to v?

Let a, b, c be three constant vectors drawn from the origin to the points A, B C. What is the distance from the origin to the plane defined by the points A, B C? What is the area of the triangle ABC?

Let us name three perpendicular directions as right, up, and toward you as you might name them when you are facing a television screen that lies in a vertical plane. Unit vectors for these directions are r, u, and t, respectively. Consider the quantity (3u2t). (i) Is the magnitude of this vector (a) 6, (b) 3, (c) 2, or (d) 0? (ii) Is the direction of this vector (a) down, (b) toward you, (c) up, (d) away from you, or (e) left?

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 .

The polar coordinates of a point are 4/3and 5.50 m. What are its Cartesian coordinates?

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.

Given the displacement vector , find the displacement vector so that .

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.

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 particle undergoes three consecutive displacements given by vectors , and . (a) Find the resultant displacement vector of the particle. (b) What is the magnitude of the resultant displacement? (c) If all displacements were along one line, how far would the particle travel?