Question
Asked Jan 26, 2020
1 views

Define the dot product (scalar product) of two vectors. Which al-gebraic laws are satisfied by dot products? Give examples. When is the dot product of two vectors equal to zero?

check_circle

Expert Answer

Step 1

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

Calculus homework question answer, step 1, image 1
fullscreen
Step 2

Algebraic laws satisfied by dot product: 

(1) (Commutative Property) For any two vectors A and B, A.B = B.A.

(2) (Scalar Multiplication Property) For any two vectors A and B and any real number c, (cA).B = A.(cB) = c(A.B)

(3) (Distributive Property) For any 3 vectors A, B and C, A.(B+C) = A.B + A.C.

Step 3

Examples for:

Commutative Property: (1,2,3).(4,5,6)=1(4)+2(5)+3(6)=4+10+18=32

(4,5,6).(1,2,3)...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Related Calculus Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: п What happens to x cos(nx)dx when n = 0? Justify your answer.

A: First of all, consider the given integral value and integrate.Let nx = a.Calculate dx and the limits...

question_answer

Q: What is the arc length function for a smooth parametrized curve? What is its arc length differential...

A: Click to see the answer

question_answer

Q: Use the identity sin^2 x = (1 - cos 2x)/2 to obtain the Maclaurin series for sin^2 x. Then different...

A: It is given that

question_answer

Q: find the component form of the vector. The vector OP where O is the origin and P is the midpoint of ...

A: Given points are R = (2, -1) and S = (-4, 3).First find midpoint P by using midpoint formula as foll...

question_answer

Q: What is a Maclaurin series?

A: The Maclaurin series of f is the Taylor series generated by,

question_answer

Q: How can you sometimes find the area bounded by a parametrized curve and one of the coordinate axes?

A: Let the equation of parametrized curve be 

question_answer

Q: Use the Euler method with dx = 0.5 to estimate y(5) if y′ = y2/sqrt(x) and y(1) =-1. What is the exa...

A: Consider the formula used in Euler’s method.Also summarize the given data in the question.

question_answer

Q: Write inequalities to describe the sets in Exercises 45–46. 45. The half-space consisting of the poi...

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

question_answer

Q: I need to compute each limit. The limit is ... lim x -> 1 x - 1  ————— 2 - the square root of x +...

A: Given: