30. Find the shortest distance from the point P(0, 1, – 1) to the line (x, y, z) = (1, 1, 0) + t(1, –1, –2). (a) / 66 (b) V65 (c) (d) v62 (e) V61

Q: (7) (a) Find the linear approximation L(x, y) to the function f(x, y) = √² + y² + 4 at the point…

A:

Q: b) Find the slope of the function f(x) = VI+1at point (15,4).

A: The slope of  f(x) at a point (a,b) or x=a and f(a)=b is given by, df(x)dxx=a or f'(a)

Q: -2+z) ds over t e point (0, 0, 0)

A:

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r"(t). P(C) = 21²1 - 48 + ²P²H 2³k r(t) 3 (a) r(t) 3it…

A:

Q: Find Duf at P. f(x, y, z) = 6x³y³z³; P(2, — 2, 2); u = Duf = i + - 2|3 k

A:

Q: Q.2 Find DivF and curlF at point (1,2) , where f(x, y) = xy² + Inxy

A:

Q: 3. Evaluate f 2xdx + (y + 2)dy along the rectangle with vertices (0, 0), (0,3), (3,3) and (0, 3).

A:

Q: A Find the value of J G dL if G = x'a, - xyza, given points P,(1,2,3) and P;(5,0,4) and a path…

A: Given: G=x2ax-xyzaz P1:1,2,3 P2:5,0,4   To find: The value of ∫P1P2G·dL for a path consisting of:…

Q: 1. Let F(t) = (e¹−¹ – ť², 3t² + 1, 4-5 lnt), G(1) = (-6, 1,0), and f(t) = cost. Evaluate: (a) (F-G)…

A:

Q: Transform the function y=(1)/(2)x right 6 and vertical shrink of (1)/(4)

A: The given function is y=12x. To transform the function rightwards by 6 units and to shrink…

Q: [10] (1) GIVEN: L: c(t) (0,1,2) FIND: The distance from B to the line, L. d(B, L). B = = (-1+ 2t,…

A:

Q: 5 B) Find y" for the function y = x + Vx at p(1,3)

A: Given query is to find the double derivative of the expression at point p.

Q: Find y as a function of a if y(1)=2, y(1) = 1. y = r²y" + 7xy +9y = 25,

A:

Q: Find the distance from the point (-3,1,0) to the line d(t) = (1, 0, 2)t + (4, – 9, – 2) .

A:

Q: Find the point (x,y) on the line y=x that is equidistant from the points (3,8) and (−10,−10)

A: To find the point x, y on the line y=x, that is equidistant from the points 3, 8 and -10, -10.