brysondennard904
Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Vector v is shown in the graph.
vector v with initial point at 0 comma 0 and terminal point at negative 8 comma 6
Which are the component form and magnitude of v?

v = ❬–8, 6❭; ||v|| = –10
v = ❬8, 6❭; ||v|| = –10
v = ❬8, 6❭; ||v|| = 10
v = ❬–8, 6❭; ||v|| = 10

Question 5
Vector v is shown in the graph.
vector v with initial point at 2 comma 5 and terminal point at negative 3 comma negative 2

Which are the magnitude and direction of v? Round the answers to the thousandths place.

||v|| = 8.602; θ = 54.462°
||v|| = 8.602; θ = 234.462°
||v|| = 9.220; θ = 54.462°
||v|| = 9.220; θ = 234.462°

Sagot :

Question 4

Answer: Choice D

Explanation:

If the initial point is the origin, the coordinates of the terminal point form the vector itself in component form. We go from (-8,6) to <-8,6>. The notation change is from ordered pair to vector format.

We have a right triangle with legs of 8 and 6 units. The pythagorean theorem will help us determine the hypotenuse is 10. Therefore, the vector length is 10 units and we would say ||v|| = 10. We have a 6-8-10 right triangle.

===========================================================

Question 5

Answer: Choice B

Explanation:

Vector v starts at (2,5) and ends at (-3,-2).

The x component of the vector is x2-x1 = -3-2 = -5 meaning we move 5 units to the left when going from the start point to the endpoint.

At the same time we move 7 units down because y2-y1 = -2-5 = -7 which is the y component of the vector.

The component form of vector v is

v = <-5, -7>

it says "move 5 units left, 7 units down".

Apply the pythagorean theorem to find the length of the vector.

a^2+b^2 = c^2

c = sqrt(a^2 + b^2)

||v|| = sqrt( (-5)^2 + (-7)^2 )

||v|| = 8.602 which is approximate.

Now let's use the arctangent function to find the angle

theta = arctan(b/a)

theta = arctan(-7/(-5))

theta = 54.462 which is also approximate.

There's a problem however. This angle is in Q1 but the vector <-5,-7> is in Q3. An easy fix is to add on 180 to rotate to the proper quadrant.

54.462+180 = 234.462

which is the proper approximate angle for theta.

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.