Vectors are said to be orthogonal if their dot product is zero.Vectors in Rn are perpendicular if they are nonzero and orthogonal.
Their sum can be zero only if their magnitudes are equal and their directions are exactly opposite.
It depends on what the dot product is meant to be equal to.
No, the zero would be too big that it would take years to finish it. Hope this helped.
When the component vectors have equal or opposite directions (sin(Θ) = 0) i.e. the vectors are parallel.
Their DIFFERENCE will be zero if and only if they have the SAME direction.
If 'A' and 'B' are vectors, and their magnitudes are equal, andtheir directions are opposite, then their vector sum is zero.
A nonzero whole number is a quantity which does not equal zero and number without fractions.
(A1) The dot product of two vectors is a scalar and the cross product is a vector? ================================== (A2) The cross product of two vectors, A and B, would be [a*b*sin(alpha)]C, where a = |A|; b = |B|; c = |C|; and C is vector that is orthogonal to A and B and oriented according to the right-hand rule (see the related link). The dot product of the two vectors, A and B, would be [a*b*cos(alpha)]. For [a*b*sin(alpha)]C to equal to [a*b*cos(alpha)], we have to have a trivial solution -- alpha = 0 and either a or b be zero, so that both expressions are zeroes but equal. ================================== Of course one is the number zero( scalar), and one is the zero vector. It is a small difference but worth mentioning. That is is to say if a or b is the zero vector, then a dot b must equal zero as a scalar. And similarly the cross product of any vector and the zero vector is the zero vector. (A3) The magnitude of the dot product is equal to the magnitude of the cross product when the angle between the vectors is 45 degrees.
A quantity which does not equal zero is said to be nonzero.
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.
Yes. A vector has magnitude and direction. If the vectors have equal magnitude and directly opposite directions their sum will be zero.
When the angle between two vectors is zero ... i.e. the vectors are parallel ... their sum is a vector in thesame direction, and with magnitude equal to the sum of the magnitudes of the two original vectors.
Two - if you add two vectors of equal magnitude but in opposite directions, the resultant vector is zero.
zero is the answer
Any number raised to the power of zero is always equal to 1
Normally you use sine theta with the cross product and cos theta with the vector product, so that the cross product of parallel vectors is zero while the dot product of vectors at right angles is zero.
The value of any nonzero number raised to the zero power will equal positive one (1).
Yes. Vectors contain both magnitude and direction. Graphically three vectors of equal magnitude added together with a zero sum would be an equilateral triangle.
Any nonzero number raised to the power of zero is equal to one (1).By definition.
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)
It is always 1
You CAN'T divide by zero.