1) 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
2) Use the figure (in the link below) to sketch a graph of the specified vector.
−4𝘃
www.webassign.net/waplots/5/a/5c643fc0ae0e4f3f1e296978adc432.gif
1) To sketch the graph of the vector 4𝘂 + 3𝘃, you can use the given figure in the link. Here's how you can do it:
- Start at the origin (0,0) on the coordinate plane.
- Move 4 units in the positive 𝘶 direction. This means moving 4 units to the right on the x-axis.
- Then, move 3 units in the positive 𝘷 direction. This means moving 3 units up on the y-axis.
- Draw an arrow from the origin to the point you ended up after moving in the 𝘶 and 𝘷 directions.
The resulting graph will be a diagonal arrow pointing upwards to the right.
2) To sketch the graph of the vector -4𝘷, you can use the given figure in the link. Here's how you can do it:
- Start at the origin (0,0) on the coordinate plane.
- Move 4 units in the negative 𝘷 direction. This means moving 4 units down on the y-axis.
- Draw an arrow from the origin to the point you ended up after moving in the negative 𝘷 direction.
The resulting graph will be a vertical arrow pointing downwards.
To sketch a graph of a vector, you can follow these steps:
1) Start by drawing the coordinate axes (x-axis and y-axis) on a graph paper or digital drawing platform.
2) Look at the vector components provided in the question. Each component represents the amount of displacement in the x-direction (horizontal) and y-direction (vertical).
3) Take the horizontal component (u or v) and draw a line segment with that length parallel to the x-axis. In this case, the horizontal component is 4u (question 1) or -4v (question 2).
4) Next, take the vertical component (v) and draw a line segment with that length parallel to the y-axis. In question 1, the vertical component is 3v, while in question 2, it is 0 since the vector has no vertical component.
5) To determine the ending point of the vector on the graph, start from the origin (0,0) and move horizontally along the x-axis according to the horizontal component, and vertically along the y-axis according to the vertical component.
Now, let's apply these steps to the given questions:
1) For the vector 4u + 3v, we see that the horizontal component is 4u and the vertical component is 3v. On the graph, draw a line segment with a length of 4 units parallel to the x-axis and 3 units parallel to the y-axis starting from the origin (0,0). Connect the starting point (0,0) with the ending point of the line segment to complete the vector representation.
2) For the vector -4v, we notice that the horizontal component is 0 since there is no horizontal displacement. The vertical component is -4v. On the graph, draw a line segment with a length of 4 units parallel to the y-axis, but in the opposite (downwards) direction. Start from the origin (0,0) and draw the line segment downwards. This line segment represents the vector -4v.
Remember, vectors have both magnitude and direction, which is why we refer to their graphical representation as "vector diagrams."
you have u and v.
So, extend u to 4 times its length
extend v to 3 times its length
use the expanded 4u and 3v as sides of a parallelogram
the desired 4u+3v is the diagonal
draw v
extend it to 4 times its length
put the arrowhead at the other end.
study the material on vectors some more!