HELP cartesian form vector help

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The discussion focuses on calculating the dot product and cross product of two vectors, A and B, expressed in Cartesian form. The vectors are A = +6X - 3Y + 4Z and B = -3X + 1Y - 5Z. The user expresses urgency for help with these calculations, especially with an upcoming test. Recommendations for helpful video resources on dot and cross products are provided, emphasizing that these concepts are manageable with practice. Overall, the conversation highlights the importance of understanding vector operations for success in the upcoming test.
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URGENT HELP! cartesian form vector help!

Homework Statement


given the following vectors, calculate Adotb and BxA. Express your answers in cartesian Form

A= +6X-3Y+4Z B= -3X+1Y-5Z

Homework Equations





The Attempt at a Solution


My teacher went over this in about five minutes making it seem like easiest thing in the world the last class before the test and told us its going to be on the test. I'm stuck now and don't know how to do these types of equations. it would also help if anybody has tips on how i would go about doing a problem like (0,5,6)--->(1,3,8). Test is tomorrow at 9, any help would be greatly appreciated!
 
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thank you! i love this guy, but i didn't know he had videos on this.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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