Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
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.
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.