Question

5. The distributive property for multiplication and addition of scalars states that if a, b and c are scalars then a &times (b + c) = (a &times b) + (a &times c) . (You learned this years ago). The distributive property for the dot product would state that if a, b and c are vectors then a &middot (b + c) = (a &middot b) + (a &middot c) Three vectors, a, b and c, are shown in the diagram below. |a| = 5, |b| = 3 and |c| = 7 . a. Draw the vector b + c and determine its magnitude and direction. b. Use your result from a) to determine a &middot (b + c) c. Use the given information and the diagram to find (a &middot b) and (a &middot c) d. Do your results show that the dot product obeys the distributive property?

          5. The distributive property for multiplication and addition of scalars states that if a, b and c are scalars then a &times (b + c) = (a &times b) + (a &times c) . (You learned this years ago).

The distributive property for the dot product would state that if a, b and c are vectors then a &middot (b + c) = (a &middot b) + (a &middot c)

Three vectors, a, b and c, are shown in the diagram below. |a| = 5, |b| = 3 and |c| = 7 .

a. Draw the vector b + c and determine its magnitude and direction.
b. Use your result from a) to determine a &middot (b + c)
c. Use the given information and the diagram to find (a &middot b) and (a &middot c)
d. Do your results show that the dot product obeys the distributive property?

Show more…

5. The distributive property for multiplication and addition of scalars states that if a, b and c are scalars then a times (b + c) = (a times b) + (a times c) . (You learned this years ago).

The distributive property for the dot product would state that if a, b and c are vectors then a middot (b + c) = (a middot b) + (a middot c)

Three vectors, a, b and c, are shown in the diagram below. |a| = 5, |b| = 3 and |c| = 7 .

a. Draw the vector b + c and determine its magnitude and direction.
b. Use your result from a) to determine a middot (b + c)
c. Use the given information and the diagram to find (a middot b) and (a middot c)
d. Do your results show that the dot product obeys the distributive property?

Added by Steven J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/26/2023

Step 1

Draw the vector b + c: To draw the vector b + c, we place the tail of vector c at the head of vector b. The resulting vector starts at the tail of b and ends at the head of c. Show more…

Show all steps

lock

Thanks for your feedback!

The distributive property for multiplication and addition of scalars states that if a, b and c are scalars then a x (b + c) = (a x b) + (a x c) . (You learned this years ago). The distributive property for the dot product would state that if a, b and c are vectors then a · (b + c) = (a · b) + (a · c) Three vectors, a, b and c, are shown in the diagram below. |a| = 5, |b| = 3 and |c| = 7 . a. Draw the vector b + c and determine its magnitude and direction. b. Use your result from a) to determine a · (b + c) c. Use the given information and the diagram to find (a · b) and (a · c) d. Do your results show that the dot product obeys the distributive property?

Play audio

Feedback

Powered by NumerAI

Madhur L and 65 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 Hello everyone, welcome to this video.

00:03 So here we are given with a vector a b c.

00:06 We have to find b plus c.

00:10 So b plus c is given by 3 plus 7.

00:15 So that will be equal to 10.

00:18 Now we have to find magnitude and direction of the vector b plus c.

00:26 So to find that let us take as magnitude is equal to b plus c.

00:35 So let us take the magnitude as v squared which is given by 3 squared plus 7 squared will be equal to 58.

00:53 So therefore the magnitude is given by root of 58.

00:59 Therefore the magnitude of vector b and c that is v is given by root 58.

01:09 The value is 7 .62.

01:13 Now we have to find the direction.

01:15 So direction we have to find the angle theta.

01:20 So angle theta we have the formula tan inverse of b by a.

01:26 So using this let us find out.

01:29 So here our tan inverse b value is given by 7 .62 and the a value which we have is 3.

01:43 So respective to the vector b and c.

01:45 So here we have tan inverse of 7 .62 by 3.

01:51 So therefore we get the theta value that is the direction is given by theta is equal to 68 .51.

02:01 Now let us find the next one.

02:03 Next we have to find a dot b plus c.

02:07 So already we have b plus c is equal to 7 and a vector is given by 3...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later