Express the vector in the form ai + bj + ck.
if A is the point (-1, -5, 4) and B is the point (4, -12, 7)
A. v = 5i - 7j - 3k
B. v = 5i + 7j + 3k
C. v = 5i - 7j + 3k
D. v = 5i + 7j - 3k
Answer: C
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Solve the problem.Find parametric equations for the normal line to the surface 
at the point 
A. 
B. 
C. 
D. 
Find the gradient field F of the function f.f(x, y, z) = ln (x6 + y7 + z7)
A. F = 
i + 
j + 
k
B. F = 
i + 
j + 
k
C. F = 
i + 
j + 
k
D. F = 
ln ( y7 + z7)i + 
ln (x6 + z7)j + 
ln ( x6 + y7)k
Provide an appropriate response.For x2 + xy + yz + z2 = 6, the partial derivative 
evaluated at x = 1, y = 2, z = 1 is
A. - 
B. -1
C. - 
D. - 
E. - 
Rewrite the equation in standard form. Find the center or vertex. Identify the conic and sketch the curve.x2 + y2 + 2x + 12y - 12 = 0
A. circle; center (-1, -6);
(x - 1)2 + (y - 6)2 = 49
B. circle; center (1, 6);
(x + 1)2 + (y + 6)2 = 49
C. circle; center (-1, -6);
(x + 1)2 + (y + 6)2 = 49
D. circle; center (1, 6);
(x - 1)2 + (y - 6)2 = 49