Vector A⃗ points in the negative x direction and has a magnitude of 22 units. The vector B⃗ points in the positive y direction.

partA:Find the magnitude of B⃗ if A⃗ +B⃗ has a magnitude of 37 units.

partB:
Sketch A⃗ and B⃗ .
Draw the vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will be graded.

ninety degrees?

B=sqrt(37^2-22^2)

Part A: To find the magnitude of B⃗, we need to subtract the magnitude of A⃗ from the magnitude of A⃗ +B⃗ .

37 units - 22 units = 15 units.

So, the magnitude of B⃗ is 15 units.

Part B: Since vector A⃗ points in the negative x direction, we can draw it as an arrow pointing to the left. And since vector B⃗ points in the positive y direction, we can draw it as an arrow pointing upwards.

Here's a sketch of the vectors A⃗ and B⃗:

|
| B⃗
|
----->
A⃗

part A:

To find the magnitude of vector B⃗, we can use the fact that A⃗ + B⃗ has a magnitude of 37 units.

The magnitude of a vector can be calculated using the Pythagorean theorem. For two perpendicular vectors, the magnitude of their sum is given by:

|A⃗ + B⃗| = √(|A⃗|^2 + |B⃗|^2)

Given that |A⃗| = 22 units, we can substitute the values into the formula:

37 = √(22^2 + |B⃗|^2)

Squaring both sides of the equation, we get:

1369 = 484 + |B⃗|^2

Simplifying further:

|B⃗|^2 = 1369 - 484
|B⃗|^2 = 885

Taking the square root of both sides:

|B⃗| = √885
|B⃗| ≈ 29.74 units

Therefore, the magnitude of vector B⃗ is approximately 29.74 units.

part B:
To sketch vector A⃗, start at an origin point and draw a line segment in the negative x-direction with a length of 22 units.

To sketch vector B⃗, start at the endpoint of vector A⃗ and draw a line segment in the positive y-direction. The length of vector B⃗ is not given, so you can make an estimation or scale it to fit your sketch.

The orientation and length of the vectors are important in this sketch, so it is recommended to use a ruler or straightedge to ensure accuracy.

It is also important to label the vectors A⃗ and B⃗ to indicate their directions and magnitudes.

Remember, the exact orientation and length of the vectors in your sketch will be graded, so try to be as accurate as possible.

Part A:

To find the magnitude of vector B⃗, we first need to determine the magnitude of the resulting vector A⃗ + B⃗, which is given as 37 units.

When we add two vectors, such as A⃗ and B⃗, the resulting vector can be found using vector addition. The magnitude of the resulting vector can be calculated using the Pythagorean theorem.

The Pythagorean theorem states that the magnitude of the resulting vector (A⃗ + B⃗) is equal to the square root of the sum of the squared magnitudes of the individual vectors.

Mathematically, it can be written as:

|A⃗ + B⃗| = √(|A⃗|^2 + |B⃗|^2)

We are given the magnitude of vector A⃗ as 22 units, and we need to find the magnitude of vector B⃗.

Let's substitute the given values into the equation:

37 units = √(22^2 + |B⃗|^2)

To solve for |B⃗|, we need to isolate it on one side of the equation. First, square both sides of the equation:

(37 units)^2 = (22^2 + |B⃗|^2)

1369 units^2 = 484 + |B⃗|^2

Next, subtract 484 from both sides of the equation:

885 units^2 = |B⃗|^2

To remove the square, we take the square root of both sides:

|B⃗| = √885 ≈ 29.73 units

Therefore, the magnitude of vector B⃗ is approximately 29.73 units.

Part B:

To sketch vector A⃗ and B⃗, we need to consider their directions and magnitudes.

Vector A⃗ points in the negative x direction, so it extends along the negative x-axis. Its magnitude is 22 units.

Vector B⃗ points in the positive y direction, so it extends vertically in the positive y-axis direction. We do not have the magnitude of vector B⃗, so we cannot determine its exact length. However, we know that |B⃗| is approximately 29.73 units (as found in Part A).

To sketch them, draw an arrow in the negative x direction with a length of 22 units, and draw another arrow in the positive y direction with a length of approximately 29.73 units. Make sure to label them as vector A⃗ and vector B⃗ respectively.

Your sketch should have vector A⃗ extending in the negative x direction with a length of 22 units and vector B⃗ extending vertically in the positive y direction with an approximate length of 29.73 units.