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Write an algebraic equation for the following The sum of twice a and four times y is equal to thirteen?
Write the following as an algebraic expression using x as the variable: The sum of a number and -8
What is the sum of 15 and w algebraic expression?
It is: 15+w or w+15 as a algebraic expression
What is algebraic sum?
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.
Prove that two vectors must have equal magnitude if their sum is perpendicular to their difference?
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.
What is the algebraic expression for the sum of 15 and the product of 5 and v?
It is: 15+5v
When is the vector sum of two vectors not equal in magnitude to their algebraic sum?
In all cases except when they act in the same direction.
When is the vector sum equal in magnitude to the algebraic sum?
When the angle between any two component vectors is either zero or 180 degrees.
How the magnitude of vector is equal to 1?
If the sum of the squares of the vector's components is ' 1 ',then the vector's magnitude is ' 1 '.
Is the sum of two vectors of equal magnitude equal to the magnitude of either vectors AND their difference root 3 times the magnitude of each vector?
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.
How can the resultant of two vecters of the same magnitude be equal to 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.
Can a magnitude of vector greater than its components?
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.
Can the sum of two vector be equal to either of the vector?
Only if one of them has a magnitude of zero, so, effectively, no.
When is the vector sum of two quatities equal in magnitude to the scalar sum?
When all the vectors have the same direction.
If two vector have equal magnitudes can their sum be zero Explain?
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.
Can the sum of two equal vectors be equal to either vector?
Only if one of them has a magnitude of zero, so, effectively, no.
What magnitude is not possible when a vector of a magnitude of 3 is added to a vector of a magnitude of 4?
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.
Can two vectors having different magnitude be combined to give a vector sum of zero?
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.
