(c) If f is a C² scalar function, then V × (Vƒ) = 0. True False (d) The lines 1₁ (t) = (1 − t, 1+ t, 2t) and 1₂ (t) = (4 - 2t, 3 + 2t, 1 + 5t) are parallel. True False

Q: Let L₁ be the line passing through the points Q1=(-4, 2, -4) and Q2-(-1, 0, -6) and let L2 be the…

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Q: Let L be the line through the point Q = (-2, 9, -4) and direction vector -[-1, 2, -2]T. Find the two…

A: The equation of the line passing through the point x1, y1, z1 and having direction ratios l, m, n is…

Q: 6. Find the symmetric equation of the line parallel to ở = (1,4, 6) + t(−2, 4, 7) that intersects…

A: Given problem:- 6. Find the symmetric equation of the line parallel to r = (1,4,6) + t(−2, 4, 7)…

Q: Show that r1(t) and r2(t) define the same line, wherer1(t) = t (2, 1, 3), r2(t) = (−6, −3, −9) + t…

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Q: f (x) = x2 – 2x + 2 | P 3 3+h an expression for the gradient of the line joining the points, P and…

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Q: Use the definition to determine whether or not =(3,5,-2)'. =(-2,1,4)', and =(1,3,7) are linearly…

A: We have to check whether given set of vector is linearly independent or dependent.

Q: 24 The line y = x - 10 intersects the curve x² + y² + 4x + 6y - 40 = 0 at the points A and B. Find…

A: Consider the given equation of curve, x2+y2+4x+6y-40=0 It is given that the line y=x-10 intersects…

Q: Which of the following pairs of lines are orthogonal (perpendicular)? 7 (a) r (1) + (6) t 2 +t (1)…

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Q: Find the distance from the point (0,1,-1) to the line a(t) = (-2, 2, 4)t + (-6, - 1,5)

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Q: 14-15) For the function f(x) = -7x +4; Find f (x+ h)-f(x). A)-7a - 7h +4 B) -7h C) -7a D) -7x - 7h…

A: In order to find the slope of tangent to the curve, we need to differentiate the function.

Q: O Find an equation for the plane through the point P = (3, −2, 4) that is perpendicular to the line…

A: Given problem:- Find an equation for the plane through the point P = (3, -2, 4) that is…

Q: Consider the function f (x) = Vx + 4. a) Apply the difference quotient to f(x) to determine the…

A: Let's find.

Q: Find Vf(a), given the following data. Calculate 91, 92 and g3 such that Vƒ(a): 91 92 93 = || || = 91…

A: The given problem is to find the grad f for the given data of directional derivative of function f…

Q: t G(u, v) = (6u + v, 32u + 9v) be a map from the uv-plane to the xy-plane. Find the image of the…

A: We have to find the equation of line in slope intercept form.

Q: Find the distance of the point (4, 2, -4) from the line r(t) = (1+2t, 1+ 2t, 7 - 3t).

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Q: Let L₁ be the line passing through the points Q₁-(-1, -3, 1) and Q₂=(-4, -6, 2). Find a value of k…

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Q: Determine the equation of the linear function, L(x), with a domain of {xx ER}, L(-7)= A(-7) and P(x)…

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Q: For the linear function f(x)= -2x-2. Describe the line slat

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Q: T/f Two parallel lines in the 2d plane never intersect each other

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Q: If (x1, yı) and (x2, y2) are distinct points in the plane, show that y 1 1 =0 X1 x2 y2 is the…

A: If (x1, y1) and (x2, y2) are distinct points in the plane, to show that  xy1x1y11x2y21 =0 is the…

Q: Find k so that the points P(0, 1, 1), Q(-1, 1, 3), and R(-3, 1, k) are on the same line (collinear).

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