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No, changing order of vectors in subtraction give different resultant so commutative and associative laws do not apply to vector subtraction.

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No.

Q: Do the commutative and associative laws apply to vector subtraction?

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No, the associative property only applies to addition and multiplication, not subtraction or division. Here is an example which shows why it cannot work with subtraction: (6-4)-2=0 6-(4-2)=4

The basic rules of algebra are as follows... * Remember when moving a constant from one side to another, you must apply new value. (ie. positive or negative number) 5+x=25/5+5-5=25-5/x=5 You must remember to isolate the unknown value (more commonly known as a variable) in order to solve an equations. 5x+4=x+20/ Group variable on one side, constants on other. 5x-x=20-4/4x=16/x=4 You may only add, subtract, multiply and/or divide coefficients and variables which are the same. (ie.x+x/2x+3x) After you have finished solving your equation, the order of variables are as follows this- alphabetical order, and then its the highest exponent sum. (ie. x+y4+z7) If requested, present a Left-Side Right-Side check. * Commutative property: a+b = b+a, ab = ba * Associative property: a+(b+c) = (a+b)+c = a+b+c, a(bc) = (ab)c = abc * Identities: a+0 = a, 1a = a * Distributive property of multiplication over addition: a(b+c) = ab+ac The first three properties have an versions for addition and multiplication. Division and subtraction are not commutative or associative. The distributive property ties addition and multiplication together. One important concept is the order of operations. Parentheses establish precedence. Multiplication and division occur first, left to right, and then addition and subtraction. Thus, 5+3x4 = 17, not 32. Other key concepts are the slope/intercept form of a line, y=mx + b, where m=slope and b=y intercept. Memorize the quadratic equation--it will prove very useful. And above all else, learn how to do ratios and proportions.

Within parentheses or similar symbols, the same rules apply as when you don't have parentheses. For example, multiplication and division have a higher priority (or precedence) than addition and subtraction.Within parentheses or similar symbols, the same rules apply as when you don't have parentheses. For example, multiplication and division have a higher priority (or precedence) than addition and subtraction.Within parentheses or similar symbols, the same rules apply as when you don't have parentheses. For example, multiplication and division have a higher priority (or precedence) than addition and subtraction.Within parentheses or similar symbols, the same rules apply as when you don't have parentheses. For example, multiplication and division have a higher priority (or precedence) than addition and subtraction.

You will apply them when solving quadratic equations in which the quadratic expression cannot be factorised.

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Yes subtraction of vector obeys commutative law because in subtraction of vector we apply head to tail rule

No!!

Both union and intersection are commutative, as well as associative.

Try it! You will probably get a negative number...

Associative works for addition and multiplication. Commutative works for addition and multiplication Distributive works for addition, multiplication and subtraction as well as some combinations of them, but not for division. Nothing works for division.

No, the associative property only applies to addition and multiplication, not subtraction or division. Here is an example which shows why it cannot work with subtraction: (6-4)-2=0 6-(4-2)=4

Vector addition is basically similar, with respect to many of its properties, to the addition of real numbers.A + B = B + ASubtraction is the inverse of addition: A - B = A + (-B), where (-B) is the opposite vector to (B).A - B is not usually the same as B - A. Therefore, it is not commutative.However, if you convert it to an addition, you can apply the commutative law: A + (-B) = (-B) + A.

there is not division for the associative property

You will already be familiar with binary operations such as addition and multiplication. These are called binary oprations because they are rules about combining two elements (numbers) to get a third element. The associative property for addition states that if you have two binary operations, the order in which you carry them out does not matter. Thus, (2 + 3) + 5 = 2 + (3 + 5) = 10 And similarly, for multiplication, (2 * 3) * 5 = 2 * (3 * 5) = 30 The commutative property for addition states that the order of the numbers does not matter. Thus, 2 + 3 = 3 + 2 = 5 And similarly, for multiplication, 2 * 3 = 3 * 2 = 6 Note that neither the associative nor the commuitative properties apply to subtraction or division.

Here is an example: 4/2 = 2 Commutative property is when you can move numbers around in a problem, and it wouldn't change. This is why it doesn't work in division 2/4 = 1/2 The commutative property applies to only addition and multiplication. It does not apply to division or subtraction. More examples: Addition: 2 + 3 = 3 + 2 = 5 Subtraction: 2 - 3 = -1, 3 - 2 = 1 Division: (see above) Multiplication: 3(5) = 5(3) = 15

No, it is not. (12 / 6) / 2 = 1, but 12 / (6 / 2) = 4.

Yes, it does.