The magnitude of the vector sum will only equal the magnitude of algebraic sum, when the vectors are pointing in the same direction.
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
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 '.
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.
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.
Yes. A vector has magnitude and direction. If the vectors have equal magnitude and directly opposite directions their sum will be zero.
Only if one of them has a magnitude of zero, so, effectively, no.
iff the angle between them is 120 degrees
Force is a vector, and so the sum of all forces acting on an object is a vector sum.
'Orthogonal' just means 'perpendicular'. You can establish that if neither vector has a component in the direction of the other one, or the sum of the squares of their magnitudes is equal to the square of the magnitude of their sum. If you have the algebraic equations for the vectors in space or on a graph, then they're perpendicular if their slopes are negative reciprocals.