Use the figure (in the link below) to sketch a graph of the specified vector.
4𝘂 + 3𝘃
www.webassign.net/waplots/e/c/4ec2140bf1a3760b8fb36ad89673e2.gif
The options are (you have open each link):
a) www.webassign.net/waplots/0/b/758fcd18e80548b2e49ae517e2f496.gif
b) www.webassign.net/waplots/0/a/bba885b3d601e17dd541da8cd9ac0c.gif
c) www.webassign.net/waplots/4/3/349a3d644048ec575c2ad187b043f5.gif
d) www.webassign.net/waplots/f/c/cb83e9d9b4b43b5861bcf83d9c04ab.gif
To sketch a graph of the vector 4𝘶 + 3𝘷 using the given figure, we need to determine the correct option that represents this vector.
By looking at the figure, each unit vector 𝘶 and 𝘷 is shown separately along the x-axis and y-axis, respectively. The given vector 4𝘶 + 3𝘷 can be understood as combining 4 units of vector 𝘶 and 3 units of vector 𝘷.
Now, let's analyze the options:
a) www.webassign.net/waplots/0/b/758fcd18e80548b2e49ae517e2f496.gif
b) www.webassign.net/waplots/0/a/bba885b3d601e17dd541da8cd9ac0c.gif
c) www.webassign.net/waplots/4/3/349a3d644048ec575c2ad187b043f5.gif
d) www.webassign.net/waplots/f/c/cb83e9d9b4b43b5861bcf83d9c04ab.gif
Option a) shows 4 units in the positive x-direction but does not include any units in the y-direction. This does not match 4𝘶 + 3𝘷, which has a component in the y-direction.
Option b) shows 3 units in the positive y-direction but does not include any units in the x-direction. This also does not match 4𝘶 + 3𝘷, which has a component in the x-direction.
Option c) shows 4 units in the positive x-direction and 3 units in the positive y-direction. This matches 4𝘶 + 3𝘷, where the vector has a component in both x and y directions. Therefore, option c) represents the correct graph of 4𝘶 + 3𝘷.
Therefore, the correct answer is c) www.webassign.net/waplots/4/3/349a3d644048ec575c2ad187b043f5.gif.
extend vector u to 4 times its length without changing the direction
extend vector v to 3 times its length without changing the direction,
Complete the parallelogram.
The diagonal will be your resultant vector.
(This would have taken you about 30 seconds to do, I bet you spent over 10 minutes
just composing your post with the attached links.)