Q: When is the vector sum not equal in magnitude to the algebraic sum?

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Write the following as an algebraic expression using x as the variable: The sum of a number and -8

It is: 15+w or w+15 as a algebraic expression

The term algebraic sum is used when the numbers you are adding include both positive an negative numbers. Ordinary sums are done with positive numbers only.

Suppose the condition stated in this problem holds for the two vectors a and b. If the sum a+b is perpendicular to the difference a-b then the dot product of these two vectors is zero: (a + b) · (a - b) = 0 Use the distributive property of the dot product to expand the left side of this equation. We get: a · a - a · b + b · a - b · b But the dot product of a vector with itself gives the magnitude squared: a · a = a2 x + a2 y + a2 z = a2 (likewise b · b = b2) and the dot product is commutative: a · b = b · a. Using these facts, we then have a2 - a · b + a · b + b2 = 0 , which gives: a2 - b2 = 0 =) a2 = b2 Since the magnitude of a vector must be a positive number, this implies a = b and so vectors a and b have the same magnitude.

It is: 15+5v

Related questions

In all cases except when they act in the same direction.

When the angle between any two component vectors is either zero or 180 degrees.

If the sum of the squares of the vector's components is ' 1 ',then the vector's magnitude is ' 1 '.

No, the statement is incorrect. The sum of two vectors of equal magnitude will not equal the magnitude of either vector. The sum of two vectors of equal magnitude will result in a new vector that is larger than the original vectors due to vector addition. The magnitude of the difference between the two vectors will be smaller than the magnitude of either vector.

If the directions of two vectors with equal magnitudes differ by 120 degrees, then the magnitude of their sum is equal to the magnitude of either vector.

No, the magnitude of a vector cannot be greater than the sum of its components. The magnitude of a vector is always equal to or less than the sum of the magnitudes of its components. This is known as the triangle inequality.

Only if one of them has a magnitude of zero, so, effectively, no.

When all the vectors have the same direction.

Sum of two vectors can only be zero if they are equal in magnitude and opposite in direction. So no two vector of unequal magnitude cannot be added to give null vector. Three vectors of equal magnitude and making an angle 120 degrees with each other gives a zero resultant.

Only if one of them has a magnitude of zero, so, effectively, no.

It is not possible to obtain a vector with a magnitude of 7 when adding vectors of magnitude 3 and 4. The resultant magnitude will be between 1 and 7, as the triangle inequality states that the magnitude of the sum of two vectors is less than or equal to the sum of their magnitudes.

Yes, two vectors with different magnitudes can be combined to give a vector sum of zero if they are in opposite directions and their magnitudes are appropriately chosen. The magnitude of one vector must be equal to the magnitude of the other vector, but in the opposite direction, to result in a vector sum of zero.