1)For the line l passing through the points (1,0,1) and (2,4,7), what is the val

Question

1)For the line l passing through the points (1,0,1) and (2,4,7), what is the value of c in the following symmetric equations for l ? x-1=y/4=(z-1)/c

2)Let a=2i+j-k and b=i+2j+3k, find an equation of the line parallel to a+b and passing through the tip of b?

3)Find the intersection point of the line r=<1,0,2>+<2,-2,1>I and the plane 3x+4y+6z=7 4)find the equation of the plane containing P(-1,2,1) and the line (x+1)/2=y/5=z-3 .

5) Describe the following coordinate surface

A) r=3

b) 0= pi

6) Consider the intersection of the paraboloid z=x2+y2 with the plane x-2y=0 . find parameterization of the curve of the intersection.

7) let u(t)=2ti+sin t j-cos t k and v(t)= i+t2 j-t k. find the derivative of the vector function u(t) X v(t) .

Explanation / Answer

1) d.r's are <x 2-x1,y2-y1,z2-z1> i.e., <2-1,4-0,7-1> or < 1,4,6 > eq. of line is

x?11=y?04=z?16

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