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The first way is graphical: draw the vectors head to tail and draw a new vector with a tail having the same tail as the first vector and having the same head as the second vector. This new vector is the sum of the two.
The other way is arithmetic: Gets the components of the vectors along a set of Cartesian axis. The ith component of the sum is the ith component of the first vector plus the ith component of the second vector.
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What is the rule for adding vectors?
The general rule for adding vectors is to hook them together "head to tail" and then draw in a resultant vector. The resultant will have the magnitude and direction that represents the sum of the two vectors that were added.
When adding two vectors at right angles is the resultant of the vectors the algebraic sum of the two vectors?
No. Vectors add at rightangle bythe pythagoran theorem: resultant sum = square root of (vector 1 squared + vector 2 squared)
Why the product of two vectors is sometime scalar and sometime vector?
Because there are two different ways of computing the product of two vectors, one of which yields a scalar quantity while the other yields a vector quantity.This isn't a "sometimes" thing: the dot product of two vectors is always scalar, while the cross product of two vectors is always a vector.
Can sum of two vectors be numeric?
No, the sum of two vectors cannot be a scalar.
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.
