Question

What geometric interpretation does the dot product have? Give examples.

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Other

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: Find the derivative of the following function and evaluate the derivative at the given value of x. f...

A: The given function is,

Q: Exercises 49–50 give equations for ellipses and tell how many units up or down and to the right or l...

A: Note: We’ll answer the 49th question since we answer only one question at a time. Please submit a ne...

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: Considel the following TUnction and its graph. f(x) = -2 Use the graph to determine the limit visual...

A: The given graph of the function is

Q: give the eccentricities of conic sections with one focus at the origin along with the directrix corr...

A: 1)Given,e = 1, y = 2 Equation of conic with eccentricity e and directrix y=k corresponding to focus ...

Q: Evaluate the limit, if it esxists. (If an answer does not exist, enter DNE.). lim x°-4I+3 x>3 X-3

A: Factor the numerator.Factor 3 so that the sum of the factors is -4Factors are -3 and -1Write -4x as ...

Q: Find an equation for the set of points equidistant from the a. xy-plane and yz-plane. b. x-axis and ...

A: a) Let (x,y,z) be such point that xy-plane and yz-plane are equidistant from it.Distance of (x,y,z) ...

Q: Show that the number 4p is the width of the parabola x2 = 4py (p>0) at the focus by showing that ...

A: Click to see the answer

Q: What is an orthogonal trajectory of a family of curves? Describe how one is found for a given family...

A: There are some conditions for the orthogonal trajectories.

Q: Use the equation ƒ(x) = ƒ(a) + ƒ′(a)(x - a) + ƒ′′(c2) /2 (x - a)2 to establish the following test. L...

A: For the given function to determine its behaviour at a critical point x=a, use second derivative tes...

Q: If u1 and u2 are orthogonal unit vec-tors and v = au1 + bu2, find v. u1 .If u1 and u2 are orthogonal...

A: given u1 and u2 are orthogonal unit vec-tors and v = au1 + bu2,

Q: Find the volume V of the described solid S. The base of S is the region enclosed by the parabola y =...

A: Click to see the answer

Q: Condense the following log expression. -2log3(xy)+4/5log3(z)^10+log3(x+1)

A: Condensing the logarithmic expression.

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: a. Use Taylor’s formula with n = 2 to find the quadratic approximation of ƒ(x) = (1 + x)^k at x = 0 ...

A: Given:Use Taylor’s formula with n = 2 to find the quadratic approximation of ƒ(x) = (1 + x)^k at x =...

Q: Find the volume using the shell method. x = 8y2, y ≥ 0, x = 8;  about y = 2

A: Given:x = 8y2, y ≥ 0, x = 8;  about y = 2

Q: What is a parabola? What are the Cartesian equations for parabo-las whose vertices lie at the origin...

A: Explanation:

Q: The region bounded on the left by the y-axis, on the right by the hyperbola x2 - y2 = 1, and above a...

A: Given,The region bounded on the left by the y-axis, on the right by the hyperbola

Q: Find derivative and evaluate the derivative at given value: f(x) = (sinx)ln5x ; a = PI/2

A: The given function is,

Q: Find the area of the parallelogram with vertices K(3, 2, 1), L(3, 5, 3), M(5, 10, 3), and N(5, 7, 1)...

A: To find the area of the given parallelogram, use the vector method which is described as.We know tha...

Q: Use the Taylor series for 1/ (1 - x2) to obtain a series for 2x/ (1 - x2)2.

A: Click to see the answer

Q: What substitutions are sometimes used to transform integrals in-volving sqrt(a2 - x2), sqrt(a2 + x2)...

A: Formulas for the given type of forms is shown below:

Q: The parabola y2 = 8x is shifted down 2 units and right 1 unit to generate the parabola ( y + 2)2 = 8...

A: Given equation of parabola after shifting

Q: The line segment joining the points (0, 1) and (2, 2) is revolved about the x-axis to generate a fru...

A: To determine the surface area of the frustum.

Q: find the component form of the vector. The vector PQ, where P = (1, 3) and Q = (2, -1)

A: Given vectors

Q: 71. The square roots, cube roots, and fourth roots of + are shown in the figure from left to right, ...

A: To determine the nth root of 1 using the pattern.

Q: find a parametrization for the curve. 1. the line segment with endpoints (-1, -3) and (4, 1)

A: Click to see the answer

Q: use I=60/13(1-e-13t/5) to express the time t as a function of the current I

A: The given function of I as a function time t is as follows.

Q: By multiplying the Taylor series for ex and sin x, find the terms through x5 of the Taylor series fo...

A: First, we need to find the terms through x5 of the Taylor series for ex sin x which is found by  mul...

Q: Refer to the figure and find the volume generated by rotating the given region about the specified l...

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

Q: Let y be the percent increase in annual US national production during a year when the unemployment r...

A: a) If we plug u=0 in y=3.5-2u then we get y=3.5 .u=0 means no change in the unemployment rate.So 3.5...

Q: A tank initially contains 100 gal of brine in which 50 lb of salt are dissolved. A brine containing ...

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for yo...

Q: Solve the equation. e4x+4e2x-21=0

A:  Let us suppose y = e2x, substitute the value of y in the given equation:

Q: let u = (3, -2) and v = (-2, 5). Find the (a) component form and (b) magnitude (length) of the vecto...

A: Since you have asked multiple questions with multiple sub-part, we will solve the first question for...

Q: In Problems 11–14 verify that the indicated function is an explicit solution of the given differenti...

A: Verify that the given function is an explicit solution of the given differential equation. Find an a...

Q: Find the distance from the line x = 2 + t, y = 1 + t, z =-(1/2) - (1/2)t to the plane x + 2y + 6z = ...

A: Direction ratio of the line x = 2 + t, y = 1 + t, z =-(1/2) - (1/2)t is (1,1, -1/2)Normal vector to ...

Q: Solve the homogeneous equations (x2 + y2) dx + xy dy = 0

A: Click to see the answer