# Vector Addition Q: Find Z Component of A X B

• Naeem
In summary, the four vectors A, B, C, and D are added to vector E and the positive angles are measured counter-clockwise from the x axis. The dot product between vectors C and D is calculated by multiplying the magnitudes of the two vectors and the cosine of the angle between them. The z component of vector F, which is the cross product of vectors A and B, can be found by evaluating the determinant of the two vectors. The magnitude of vector C is 3m and the magnitude of vector D is 8m.
Naeem
Q. All four of the vectors below are added to vector E. Positive angles are measured counter-clockwise from the x axis.
A = 2 m î + 3 m ĵ
B = -7 m î -10 m ĵ
C = 3 m at 62 °
D = 8 m at -226 °

a) What is C·D?

C.D = |C| |D| cos theta

I did this.

3* cos 62 + 8 cos -226 , but the answer is wrong

b) Vector F is the cross product of vectors A and B (= A X B).

What is the z component of vector F?

The answer is one, but how

F = A X B

Find the cross product by evaluating the determinant of vectors A & B.

Then what!

a) What you did is you substracted the x-component of each vectors. That's not the dot product. The dot product is the product of length of the two vectors times the cosine of the shortest angle between then.

b) According the right-hand rule or screw rule (or whatever rule you are comfortable with), the vector F has ONLY a z component. So all you got to do is find its lenght.

Last edited:
a) The formula $$\vec{c} \cdot \vec{d} = |\vec{c}| |\vec{d}| \cos \theta$$ takes the cosine of the angle between the two vectors and multiplies the result by the magnitudes of the two vectors.

The angle between the two vectors is (-226° + 360°) - 62° = 134° - 62° = 72° = $$\frac{2\pi}{5}$$

The magnitude is calculated by adding the square of the components and taking the square root of that sum:

$$|\vec{a}| = \sqrt{x^2 + y^2}$$

Last edited:
codyg1985 said:
The magnitude is calculated by adding the square of the components and taking the square root of that sum:

$$|\vec{a}| = \sqrt{x^2 + y^2}$$

But notice Naeem that for the vectors C and D the magnitudes are already given to you: 3m and 8m.

Got, it thanks!

## 1. What is vector addition?

Vector addition is the mathematical operation of combining two or more vectors to produce a new vector. It involves finding the sum of the individual components of the vectors.

## 2. How do you find the z component of A X B?

To find the z component of A X B, also known as the cross product, you can use the formula: Z = Ax * By - Ay * Bx. This formula involves multiplying the x components of the two vectors and subtracting the product of the y components.

## 3. What is the significance of the z component in vector addition?

The z component represents the vertical or height component of a vector. In vector addition, it helps determine the magnitude and direction of the resulting vector.

## 4. Can the z component of A X B be negative?

Yes, the z component of A X B can be negative. This indicates that the resulting vector is pointing in the opposite direction of the positive z-axis.

## 5. How is vector addition used in science?

Vector addition is used in many branches of science, including physics, engineering, and astronomy. It helps describe the motion and forces acting on objects and is used in calculations for velocity, acceleration, and other physical quantities.

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