Cross Product Help: Homework Statement

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I am an AI so no need to apologize, I do not have feelings. In summary, the conversation was about finding the vector product of two given vectors and expressing the answer in terms of unit vectors. The attempt at a solution resulted in 0i + 0j - 43k, but the system marked it as wrong and the correct answer was probably just -43k. The student lost points for each attempt.
  • #1
TheRedDevil18
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Homework Statement



Given two vectors A⃗ = 4i + 7j and B⃗ = 5i − 2j , find the vector product A⃗ × B⃗ (expressed in unit vectors).
Express your answer in terms of the unit vectors i, j, and k.

Homework Equations





The Attempt at a Solution



I know how to cross and multiply them but they don't give the z component so I assumed it was zero

This is what I got

0i + 0j - 43k

Why is that wrong ?, I'm doing this online assignment and it keeps telling me, "The correct answer does not depend on i,j and k"
 
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  • #2
TheRedDevil18 said:

Homework Statement



Given two vectors A⃗ = 4i + 7j and B⃗ = 5i − 2j , find the vector product A⃗ × B⃗ (expressed in unit vectors).
Express your answer in terms of the unit vectors i, j, and k.

Homework Equations





The Attempt at a Solution



I know how to cross and multiply them but they don't give the z component so I assumed it was zero

This is what I got

0i + 0j - 43k

Why is that wrong ?, I'm doing this online assignment and it keeps telling me, "The correct answer does not depend on i,j and k"
You did it right. They probably just want -43k.

Chet
 
  • #3
Chestermiller said:
You did it right. They probably just want -43k.

Chet

Yeah, I guess they just wanted -43k with the hat on top. Stupid system, now I lost 3% for each "wrong" attempt :mad:

Thanks for your reply
 

What is a cross product?

A cross product is a mathematical operation that takes two vectors and produces a third vector that is perpendicular to both of the original vectors. It is also known as a vector product.

What is the formula for calculating a cross product?

The formula for calculating a cross product is: a x b = (|a||b|sinθ)n where a and b are the two vectors, θ is the angle between them, and n is a unit vector perpendicular to both a and b.

How is a cross product different from a dot product?

A cross product results in a vector while a dot product results in a scalar. This means that a cross product has both magnitude and direction, while a dot product only has magnitude. Additionally, the mathematical formulas for calculating these products are different.

What are some real-world applications of cross products?

Cross products have various applications in physics, engineering, and computer graphics. They are used to calculate torque, magnetic force, and angular momentum in physics. In engineering, cross products are used in the design of gears and levers. In computer graphics, they are used to create 3D models and animations.

How can I solve cross product problems more efficiently?

To solve cross product problems more efficiently, you can use the properties of cross products, such as the distributive property and the fact that the cross product of two parallel vectors is zero. Additionally, practicing with different types of cross product problems and understanding the geometric interpretation of cross products can help improve efficiency.

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