prove this force are conserved F(x,y)=2a(x-y)i-a(2x-y)j Where a is constant

A circular area S is concentric with the origin, has radius a, and lies in the yz-plane. Calculate s E ndA for E=2z2i.

If the cross product of two vectors vanishes, what can you say about their directions?

Show that (BC)A is the volume of the parallelepiped, with edges formed by the three vectors in the following figure.

In a later chapter, you will find that the weight of a particle varies with altitude such that w=mgr02r2where r0is the radius of Earth and ris the distance from Earth’s center. If the particle is fired vertically with velocity v0from Earth’s surface, determine its velocity as a function of position r. (Hint: use adr=vdv, the rearrangement mentioned in the text.)

Find the angle between vectors for (a) D=(-3.0i-4.0j)m and A=(-3.0i+4.0j)m and (b) D=(2.0i+4.0j+K)m and B=(-2.0i+3.0j+2.0K)m .

Check Your Understanding Why not use the simpler expression U=mg(y2y1) ? How significant would the error be? (Recall the previous result, in Example 13.4, that the value g at 400 km above the Earth is 8.67m/s2 .)

Show that the force vector is orthogonal to the force vector

Find the angles that vector makes with the and axes.

Show that when A+B=C then A2+B2+2ABcos , where is the angle between vectors A and B .