1. for the following vectors U=ux (ax)+ 5 (ay) - (az), V=2(ax)-Vy(ay)+ 3(az), W=

Question

1. for the following vectors U=ux (ax)+ 5 (ay) - (az), V=2(ax)-Vy(ay)+ 3(az), W=6 (ax)+(ay)+Wz (az)

obtain Ux,Vy, Wz such that

1.1 U,V,W are mutually orthogonsl

1.2 U,V and are perpendicular.

2.If E and F are vector fields given by:E=2x (ax) + (ay)+yz (az), F=xy (ax)-y^2 (ax) +xyz (az)

2.1 magnitude of E at (1,2,3)

2.2 find the component of E along F at 1,2,3

2.3 calculat2 a vector perpendicular to both E anf F t 0,1,-3 whose maginutude is unity.

Explanation / Answer

Any two vectors are orthogonal when their dot product is zero, so for U,V,W to be perpendicular U.V=V.W=W.U=0 U.V=0 implies that 2ux(ax.ax)-5VY(ay.ay)-3=0 => 2Ux-5Uy-3=0 sililarly V.W=0 gives 12-Vy+3Wz=0 and W.U=0 gives 6Ux+5-Wz=0

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