Question

can two non zero vectors give zero resultant when they multiply with each other ? if yes given the condition for the same​

Answer 1

there are two possible way of multiplications.

1. dot product and cross product.

case 1 :- Let A and B two non zero vectors and R is resultant when they multiply each other.

in case of dot product , R = |A|.|B|cos∅

R = 0 when cos∅ = 0 or ∅ = 90°

hence, resultant becomes zero in dot product only when angle between given vectors must be 90°.

case 2 : in case of cross product , R = A × B = |A|.|B|sin∅ $\cap{n}$

here it is clear that resultant of cross product will be zero when angle between given vectors must be zero.

hence, condition is ...

1. scaler multiply (or dot product) : ∅ = 90°

2. vector multiply (or cross product) : ∅ = 0°

Answer 2

Well when you asked about multiplication, you did not mention which type of vector multiplication you are talking about. So, let me explain both for you:

1:Cross product: If a and b are two vectors, then cross product between them is defined by a×b = |a|*|b|*sinΘ, where Θ is the angle between a and b. In this case product can be zero in a case where Θ= 0°, or the vectors are parallel.

2:Dot product: Dot product between two vectors a and b is defined as :

a.b = |a|*|b|*cosΘ, In this case product can be zero if Θ = 90°, or the vectors are perpendicular irrespective of values of vectors in both the cases.