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Q: Let u = 5i - j + k, v = j - 5k, w =-15i + 3j - 3k. Which vectors, if any, are (a) perpendicular? (b)...

A: To determine the vector which are,Part (a) ParallelPart (b) Perpendicular

Q: find the one-sided limit ( if it exists)

A: The given limit is,

Q: Find a vector 5 units long in the direction opposite to the direction of v = (3/5)i + (4/5)k.

A: Given:

Q: Find the work done by a force F = 5i (mag-nitude 5 N) in moving an object along the line from the or...

A: Given,

Q: Find the distance from the point (-2, 1, 4) to the a. plane x = 3 b. plane y =-5 c. plane z =-1

A: Given:The point (-2, 1, 4).Formula:The distance between a point (x1, y1, z1) and the plane  is,

Q: How do you find the intersection of two lines in space? A line and a plane? Two planes? Give example...

A: Explanation:

Q: In Exercises 1–3, find a. v. u,| v|,|u| b. the cosine of the angle between v and u c. the scalar com...

A: Hey, since there are multiple questions posted, we will answer first question. If you want any speci...

Q: Here is another typi-cal problem in computer graphics. Your eye is at (4, 0, 0). You are looking at ...

A: Given,Eye position = (4, 0, 0)Triangle plate vertices = (1, 0, 1), (1, 1, 0) and (-2, 2, 2)Line segm...

Q: Find the point on the sphere x2 + (y - 3)2 + (z + 5)2 = 4 nearest a. the xy-plane. b. the point (0, ...

A: Consider the given equation of the sphere.

Q: Find the length of the curve r(t) = (sqrt(2)t)i + (srqt(2)t)j + (1 - t2)k from (0, 0, 1) to (sqrt(2)...

A: Given curve

Q: Find the sum -2 - 2+ 3 9. 27 81 Answer:

A: Given series is a geometric series with

Q: express each vector in the form v = y1i + y2j + y3k. 5u - v if u = <1, 1, -1>and v = <2, 0,...

A: Given vectors

Q: Simplify radicals and exponents

A: For division subtract the exponents. 1/2= 2^-1

Q: Given nonzero vectors u, v, and w, use dot product and cross product notation, as appropriate, to de...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: Use the factor theorem to decide whether or not the second polynomial is a factor of the first. 4) 7...

A:

Q: Find the distance from the point (4, 3, 0) to the a. x-axis b. y-axis c. z-axis

A: To determine the distance of the point from,Part (a) x-axisPart (b) y-axisPart (c) z-axis

Q: Find the point in which the line through P(3, 2, 1) normal to the plane 2x - y + 2z =-2 meets the pl...

A: Direction ratios of normal to plane 2x - y + 2z =-2  are <2,-1,2>, since line is normal to pla...

Q: Please see attached question from my study guide. It has been a while since I took calculus 1 and ca...

A: Given,Area of the region A, B and C is 3.Since the given figure is symmetric.

Q: f(x) =16 − x2, g(x) = x + 2 Find (f + g)(x)

A: Given functions are

Q: n Exercises 39–41, find the distance from the point to the plane. 39. (2, -3, 4), x + 2y + 2z = 13 4...

A: Given, (2, -3, 4), x + 2y + 2z = 13.

Q: Find a vector of magnitude 7 in the direction of v = 12i - 5k

A: Given vector is v = 12i – 5k. First find the direction of the given vector

Q: Plot the surfaces in Exercises 49–51 over the indicated domains. If you can, rotate the surface into...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Describe the interval(s) on which the function is continuous. (Enter your answer using interval nota...

A: Consider the provided function,f(x) = (x+8)/(square root x)The rational function is continuous every...

Q: Find equations for the planes in Exercises 21–22. 21. The plane through P0(2, 4, 5) perpendicular to...

A: Since you have submitted two questions, we'll answer the first question. For the second question ple...

Q: Evaluate the integral by using a substitution prior to integration by parts. 9 sin ( In (8x)) dx 9 s...

A: To integrate

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

A: Given:

Q: Express the vectors in Exercises 9–10 in terms of their lengths and directions. 9. 22i + 22j  10. -i...

A: Since you have submitted two questions, we'll answer the first question. For the second question ple...

Q: Find the areas of the triangles whose vertices are given in Exercises 41–47. 41. A(0, 0), B(-2, 3), ...

A: Since we only answer up to 1 question, we’ll answer the first question. Please resubmit the question...

Q: For Exercises 75-78, shade the area in the complex plane. 75. (z = a + bila < 3, b 2 2) 76. (z = a +...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Show that the center of the osculating circle for the parabola y = x2 at the point (a, a2) is locate...

A: We need to show that the centre of the osculating circle for the parabola y = x2 at the point (a, a2...

Q: generate a parametrization of the line through P(2, -4, 7) parallel to v1 = 2i - j + 3k. Then genera...

A: We know that equation of line through (x1,y1,z1)  and parallel to ai+bj+ck is

Q: Let y(x) = ax2 + bx + c. The function y(x) is not invertible, however, like the function f(x) = x2 w...

A: Given:

Q: The graph of (x/a) + (y/b) + (z/c) = 1 is a plane for any non-zero numbers a, b, and c. Which planes...

A: The graph of given plane is,

Q: Given that A is a 2×4 matrix, B is a 3×4 matrix, C is a 3×2 matrix, and D is a 4×3 matrix, determine...

A: Given: A is a 2×4 matrix, B is a 3×4 matrix, C is a 3×2 matrix, and D is a 4×3 matrix.

Q: | 12f(x) + 3g(x)]dX 0. 50. Find f(x) dx if for x 3 51. For the function f whose graph is shown, li ...

A: Break the integration in two parts.One from 0 to 3, other from 3 to 5.

Q: What points in the xy-plane satisfy the equations and inequalities in Exercises 11–12? Draw a figure...

A: Since you have submitted two questions, we\'ll answer the first question. For the second question pl...

Q: Find the points in which the line x = 1 + 2t, y =-1 - t, z = 3t meets the coordinate planes. Describ...

A: The given lines are,

Q: Describe the x-values at which f is differentiable. (Enter your answer using interval notation.) (x²...

A: Consider the provided graph of the given function,Here take some point where graph of the function i...

Q: 2x and the interval - 1<x<1 of the x-axis. Find the area, A, of the region between the curve y = 1+x...

A: Find the area of the region bounded by the curves

Q: 1. (2 points) State the formula for the area of an equilateral triangle with side length a. 2. (13 p...

A: Given:An equilateral triangle with side length a.

Q: Show that a projectile attains three-quarters of its maximum height in half the time it takes to rea...

A: Show that a projectile attains three-quarters of its maximum height in half the time it takes to rea...

Q: If u * v = u * w and u ≠ 0, then does v = w? Give reasons for your answer.

A: GivenIf u * v = u * w and u ≠ 0, then does v = w? Give reasons for your answer.

Q: Find an equation for the set of points equidistant from the y-axis and the plane z = 6.

A: The formula for distance between two points (x, y, z) and (a, b, c) is

Q: evaluate the definite integral from 0 to (1/3) of pi*tan(pi*x)dx

A: Given expression is,

Q: Find parametric equations for the lines in Exercises 1–4. 1. The line through the origin parallel to...

A: Hey, since there are multiple questions posted, we will answer the first two questions. If you want ...

Q: Show that the vector v = ai + bj is parallel to the line bx - ay = c by establishing that the slope ...

A: We first have to find the slope of the given vector and the line. If the slopes are equal then they ...

Q: If vector AB = i + 4j - 2k and B is the point (5, 1, 3), find A.

A: Given,

Q: describe the given set with a single equation or with a pair of equations.The set of points in space...

A: Let the points are given by (x,y,z) 

Q: What can be said about the torsion of a smooth plane curve r(t) = ƒ(t)i + g(t)j? Give reasons for yo...

A: Given,

Q: Define the dot product (scalar product) of two vectors. Which al-gebraic laws are satisfied by dot p...

A: Let (a1,a2,a3,....) and (b1,b2,b3,...) are two vectors. Then the dot product is defined by:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.