F)The vector (1,-2,5) is perpendicular to the plane 2 4y + 10z 17. G) The functi
ID: 2886145 • Letter: F
Question
F)The vector (1,-2,5) is perpendicular to the plane 2 4y + 10z 17. G) The function h(r,y H) lim ' sin(re) (y)-+(0,0) 2 y2 If f f(x. y), then Da(z, y) (V) u Vg(x, y, z) is parallel to the surface g(a, y, z) 0. The function g(u, v) u cos(v) satisfies the equation cos(v)9 - (sin()) If f(z, y) has the property that fy(x, y) 0 always, then f must be a constant. (J)V K) 1. (L) If f(x, y)-/(?, x), then f, (z, y)-f,(z, y) when both are defined. A function f(x, y) can be continuous at (ro, yo), but not be defined at (o, Jo).Explanation / Answer
F) The vector < 1, -2 , 5> has direction ratios < 1,-2,5>
Similarly the plane's equation is 2x - 4y + 10z = 17;
Hence the direction raiots of normal to this plane are < 2, -4, 10> ;
We can see that both direction ratios are in proportion;
2/1 = -4/-2 = 10/5 = 2;
Thus, if direction ratios are in proportion, then the lines are parallel;
Thus, the vector is parallel to the normal to the plane ; And we know that normal to the plane is perpendicular to the plane;
Thus, the given vector is perpendicular to the plane;
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