# Cross product and dot product scalars

• TS656577
In summary, the problem involves calculating the dot product of the sum of two vectors (d1 and d2) and the cross product of d1 and 4d2. The final answer should be a scalar, which can be computed by multiplying the components of the cross product and adding them together. One should be careful to correctly calculate the cross product and use the correct signs in the dot product calculation.
TS656577

## Homework Statement

If d1 = 4i - 10j + 2k and d2 = 9i - 10j + 6k, then what is (d1 + d2) · (d1 × 4d2)?

## Homework Equations

Know how to do the cross product and dot product

## The Attempt at a Solution

For the answer i got 9.6i + 56j -127.68k. How do i express that as a scalar for an online program that only has one box to type in?

Your answer should be a scalar anyway if you had to take the dot product (commonly known as the scalar product). I suggest you check your answer.

I didnt think my answer was wrong though?

If you take the dot product of two vectors then the answer will be a scalar not a vector. If you post what you've done it'll be easier to identify where you went wrong.

First i calculated the quantity of d1+d2 and got 13i + 0j +8k. Then i went to the other side of the problem and distributed the 4 to the d2 terms and got a result of 36i - 40j + 24k. After that, i took the cross product of d1 and 4d2 and got -160i -24j - 200k. Then i took the dot product and got -2080i - 1600k (sorry i posted the wrong answer the first time, my bad)

For the addition of d1 and d2, -10 +(-10) does not equal 0.

For the cross product, that should be +200k.

The dot product of two vectors is:

$$\mathbf{a}\cdot \mathbf{b} = a_x b_x + a_y b_y + a_z b_z$$

Last edited:
so then when i add that up, it equals one number? for example if i had axbx=3, ayby=4 and azbz=2, then i would have something that resembles 3+4+2 and would i use 9 for the answer?

yes, that's correct.

i got -3200 for my final answer, but that seems wrong..

Again if you post exactly what you've done when computing the dot product it will be easier to advise you where you went wrong.

after doing the cross product for d1xd2, i got -160i -24j -200k. After that, i multiplied by the sum i got for the d1+d2 section. So in the end, i multiplied -160 times 13, -24 times -20, and -200 times 8. Then i had -2080 + 480 - 1600

If you look in my previous post I said that after the cross product you should have +200k not -200k.

TS656577 said:

## Homework Statement

If d1 = 4i - 10j + 2k and d2 = 9i - 10j + 6k, then what is (d1 + d2) · (d1 × 4d2)?

## Homework Equations

Know how to do the cross product and dot product

## The Attempt at a Solution

For the answer i got 9.6i + 56j -127.68k. How do i express that as a scalar for an online program that only has one box to type in?

remeber that the cross product is something like;

[-,-]: VxV----->V; \\ V=vector space

so gives you back another vector;

while the dot product (generally an inner product) is something like;

(-,-): VxV------>C \\ C=complex field

know how to make both in an euclidean orthonormal basis and you'll get your answer;

regards;
marco;

got it, thanks guys...sorry for bein dumb (sick last few days)

## 1. What is a cross product scalar?

A cross product scalar is a mathematical operation that results in a scalar quantity, or a single number, when two vectors are multiplied together. It is also known as a dot product scalar.

## 2. How is the cross product scalar calculated?

The cross product scalar is calculated by taking the dot product of two vectors and then multiplying it by the magnitude of one vector and the sine of the angle between the two vectors. The formula is: scalar = ||a|| * ||b|| * sin(theta).

## 3. What is the difference between a cross product scalar and a dot product scalar?

A cross product scalar is a vector operation that results in a scalar quantity, while a dot product scalar is a scalar operation that results in a scalar quantity. In other words, the cross product scalar takes two vectors and produces a single number, while the dot product scalar takes two scalars and produces a single number.

## 4. What are the uses of cross product and dot product scalars in science?

Cross product and dot product scalars are commonly used in physics, engineering, and other scientific fields to calculate work, force, energy, and other physical quantities. They are also used in computer graphics to determine the direction and intensity of light in a 3D space.

## 5. Can the cross product scalar or dot product scalar be negative?

Yes, both the cross product scalar and dot product scalar can be negative. This indicates the direction and orientation of the resulting vector in relation to the original vectors. A negative cross product scalar means the resulting vector is pointing in the opposite direction of the right-hand rule, while a negative dot product scalar means the vectors are pointing in opposite directions.

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