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What is a nonzero number?
A quantity which does not equal zero is said to be nonzero.
Any nonzero number raised to the power of zero is equal to?
Any nonzero number raised to the power of zero is equal to one (1).By definition.
What does any nonzero raised to the zero power equal?
Any number raised to the power of zero is always equal to 1
Why the product of nonzero rational number and a rational number is an irrational?
Actually the product of a nonzero rational number and another rational number will always be rational.The product of a nonzero rational number and an IRrational number will always be irrational. (You have to include the "nonzero" caveat because zero times an irrational number is zero, which is rational)
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.
Can the dot product of two nonzero vectors be equal to zero?
Yes, if the dot product of two nonzero vectors v1 and v2 is nonzero, then this tells us that v1 is PERPENDICULAR to v2. :)
What is the importance of a dot product being equal to zero?
Vectors are said to be orthogonal if their dot product is zero.Vectors in Rn are perpendicular if they are nonzero and orthogonal.
Can A plus B equal zero when A and B have nonzero magnitudes?
If 'A' and 'B' are vectors, and their magnitudes are equal, andtheir directions are opposite, then their vector sum is zero.
Two vectors have nonzero magnitudeunder what conditions will their sum be zero?
Their sum can be zero only if their magnitudes are equal and their directions are exactly opposite.
When are vectors said to be perpendicular?
Perpendicular means that the angle between the two vectors is 90 degrees - a right angle. If you have the vectors as components, just take the dot product - if the dot product is zero, that means either that the vectors are perpendicular, or that one of the vectors has a magnitude of zero.
A vedtor which is perpendicular to every vector?
The zero vector is not perpendicular to all vectors, but it is orthogonal to all vectors.
What is the dot product of two perpendicular vectors?
zero is the answer
Two vectors have nonzero magnitudeunder what conditions will their difference be zero?
Their DIFFERENCE will be zero if and only if they have the SAME direction.
Dot product of two perpendicular vectors?
Zero.
What is the difference between orthogonal and orthonormal vectors?
All vectors that are perpendicular (their dot product is zero) are orthogonal vectors.Orthonormal vectors are orthogonal unit vectors. Vectors are only orthonormal if they are both perpendicular have have a length of 1.
What is a nonzero number?
A quantity which does not equal zero is said to be nonzero.
What is a nonzero whole number?
A nonzero whole number is a quantity which does not equal zero and number without fractions.
