Vector vector A has a magnitude of 27 units and points in the positive y-direction. When vector vector B is added to vector A , the resultant vector vector A + vector B points in the negative y-direction with a magnitude of 18 units. Find the magnitude of vector B ?

Since both is in y-axis (+ and -) you can use the magnitude of the resultant as the sum of the magnitudes of the two vectors A and B. (from Maazul H)

A= 27 units
B=?
A+B= 18 units (- y-axis)

27+B= -18 units (+ y-axis)
B= -18-27
B= -45
The magnitude of vector B is 45 units

Why did the vectors go on a double date? Because they wanted to find their magnitude-te! Okay, enough clowning around. Let's solve this problem.

We know that vector A has a magnitude of 27 units and points in the positive y-direction. When vector B is added to vector A, the resultant vector A + B points in the negative y-direction with a magnitude of 18 units.

To find the magnitude of vector B, we can use the Pythagorean theorem. Since vector A points in the positive y-direction and the resultant vector points in the negative y-direction, vector B must have a component in the negative y-direction.

Let's assume the magnitude of vector B is 'b' and its component in the negative y-direction is 'b_y'.

Using the Pythagorean theorem, we have:
(27)^2 + (b_y)^2 = (18)^2

Simplifying:

729 + (b_y)^2 = 324

Subtracting 324 from both sides:

(b_y)^2 = 324 - 729

(b_y)^2 = -405

Uh-oh! We have stumbled upon a problem because the square of any real number cannot be negative. It seems something went awry while solving the problem.

Let me try again:
Why did the vector bring a ladder to the party? Because it wanted to scale things up!

All joking aside, it seems there might be an error or inconsistency in the given information. The magnitude of vector B cannot be determined based on the information provided.

To find the magnitude of vector B, we can consider the magnitudes and directions of vector A and the resultant vector A + B.

Given:
Magnitude of vector A = 27 units (positive y-direction)
Magnitude of resultant vector A + B = 18 units (negative y-direction)

Since the magnitude of a vector is always positive, we can ignore the negative sign for the resultant magnitude.

So, the magnitude of vector B is the difference between the magnitudes of vector A and the resultant vector:

Magnitude of vector B = Magnitude of vector A - Magnitude of resultant vector
= 27 units - 18 units
= 9 units

Therefore, the magnitude of vector B is 9 units.

To solve this problem, we can use vector addition and knowledge of vector magnitudes.

Let's denote vector A as A and vector B as B.

Given information:
Magnitude of vector A = 27 units, pointing in positive y-direction.
Magnitude of resultant vector A + B = 18 units, pointing in negative y-direction.

We can break down vector A into its components. Since vector A points in the positive y-direction, its y-component (Ay) will be positive and its x-component (Ax) will be zero.

Now, let's consider the resultant vector A + B. Since the resultant vector points in the negative y-direction, its y-component will be negative. Let's call this y-component (A + B)y.

The magnitude of the vector A + B is given as 18 units. We can use this magnitude to find the y-component of vector B (By) since the x-component of vector B (Bx) is zero.

We can use the Pythagorean theorem to relate the magnitudes of vector A and vector B to the magnitude of the resultant vector:

Magnitude of vector A + Magnitude of vector B = Magnitude of resultant vector

|A| + |B| = |A + B|
27 + |B| = 18

Now, let's solve for |B|:

|B| = 18 - 27
|B| = -9

Since magnitudes cannot be negative, we take the absolute value of -9:

|B| = 9

Therefore, the magnitude of vector B is 9 units.