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Can the magnitude of a vector be equal to one of its components?
Yes. A vector in two dimensions is broken into two components, a vector in three dimensions broken into three components, etc... If the value of all but one component of a vector equal zero then the magnitude of the vector is equal to the non-zero component.
Is it possible for vector A plus vector B to equal vector A - vector B?
It's impossible as the addition of two vectors is commutative i.e. A+B = B+A.For subtraction of two vectors, you have to subtract a vector B from vector A.The subtraction of the vector B from A is equivalent to the addition of (-B) with A, i.e. A-B = A+(-B).
What is the least number of non-zero vectors that can be added to give a resultant equal to zero?
Two - if you add two vectors of equal magnitude but in opposite directions, the resultant vector is zero.
What are those two vectors whose resultant vector is zero?
equal and opposite
Does the subtraction of two vectors obey the commutative law?
Yes subtraction of vector obeys commutative law because in subtraction of vector we apply head to tail rule
Can the magnitude of a vector be equal to one of its components?
Yes. A vector in two dimensions is broken into two components, a vector in three dimensions broken into three components, etc... If the value of all but one component of a vector equal zero then the magnitude of the vector is equal to the non-zero component.
Is it possible for vector A plus vector B to equal vector A - vector B?
It's impossible as the addition of two vectors is commutative i.e. A+B = B+A.For subtraction of two vectors, you have to subtract a vector B from vector A.The subtraction of the vector B from A is equivalent to the addition of (-B) with A, i.e. A-B = A+(-B).
When two equal and opposite vectors are added their resultant vector has zero magnitude what is the direction of this resultant?
The zero-vector has no direction.
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.
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.
What is the least number of non-zero vectors that can be added to give a resultant equal to zero?
Two - if you add two vectors of equal magnitude but in opposite directions, the resultant vector is zero.
What are those two vectors whose resultant vector is zero?
equal and opposite
Does the subtraction of two vectors obey the commutative law?
Yes subtraction of vector obeys commutative law because in subtraction of vector we apply head to tail rule
Can the resultant of two vectors be equal to zero?
Yes. A vector has magnitude and direction. If the vectors have equal magnitude and directly opposite directions their sum will be zero.
What is the minimum number of unequal forces whose vector sum can equal zero?
Three. Equal forces, two.
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.
Can two vectors of unequal magnitude add up to give the zero vector?
No. The vector resultant of addition of vectors is the vector that would connect the tail of the first vector to the head of the last. For any set of vectors to add to the zero vector, the endpoint of the last vector added must be coincident with the start point of the first. Therefore for the sum of only two vectors to have a chance of being the zero vector, the second vector must be in a direction exactly opposite the first. So you can tell that the result of adding the two vectors could only can be zero vector if the two vectors were of two equal magnitude.
