- #1

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1. proove that; p x ( q + r ) = p x q + p x r

2. and p x ( q x r ) = ( p x q ) x r

where;

p = p1i + p2j + p3k

q = q1i + q2j + q3k

r = r1i + r2j + r3k

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This is also true for multiplication.Number 2. In the second part of the question, the author is asking about the cross product between two vectors, px(qxr), and whether or not it is distributive. According to the distributivity of the cross product, if q=p, then px(pxr)=(pxp)xr. This means that (pxp)=0. Finally, this also means that the statement "px(qxr) = (pxq)xr" is not always true.

- #1

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1. proove that; p x ( q + r ) = p x q + p x r

2. and p x ( q x r ) = ( p x q ) x r

where;

p = p1i + p2j + p3k

q = q1i + q2j + q3k

r = r1i + r2j + r3k

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- #2

Staff Emeritus

Science Advisor

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Well, start with telling us what you know. What is the cross product between two vectors?

- #3

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Sounds like homework.

Do you know the result of these expressions: i x i , i x j, etc... , ?

Do you know the result of these expressions: i x i , i x j, etc... , ?

- #4

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i have left handside p x (q + r) = (p1i + p2j + p3k)( (q1+ r1)i + (q2+ r2)j + (q3+ r3)k)

am i on the right track?

- #5

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Don't forget these important symbols.

- #6

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thanks i don't know where to go from there

- #7

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chocbizkt said:thanks i don't know where to go from there

Can you now explicitly calculate the cross-product of two vectors?

- #8

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Cross product is not associative, so i don't see how

px(qxr) = (pxq)xr

px(qxr) = (pxq)xr

- #9

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- #10

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if you let q=p

then px(pxr)=(pxp)xr

such that (pxp)=0

therefore its not true statement

- #11

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chocbizkt said:yes well so far for Qn1.

i have left handside p x (q + r) = (p1i + p2j + p3k) x ( (q1+ r1)i + (q2+ r2)j + (q3+ r3)k)

am i on the right track?

Just grind through that. By that I mean set up the determinant and perform the algebra.

- #12

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SeReNiTy said:Cross product is not associative, so i don't see how

px(qxr) = (pxq)xr

Then wat is distributive law?

Vinodh

- #13

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Vinodh said:Then wat is distributive law?

Vinodh

Number 1. in the original post is the distributivity (under addition) of the cross product: i.e. ax(b+c)=axb +axc

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