- #1
draotic
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Homework Statement
Vector 'A' is along postive z-axis and its vector product with another vector 'B' is zero , then vector 'B' could be ..
a) i + j
b) 4i
c) i + k
d) -7k
.
wbandersonjr said:What do you think? What have you tried, or what equations are useful?
tiny-tim said:hi draotic!
what is the cross product (vector product) of A with each of those four vectors?
hence theta=0 degree
wbandersonjr said:This is not necessarily true. [itex]\Theta[/itex] could be 180 also, or someother multiple of [itex]\pi[/itex].
But since sin[itex]\Theta[/itex] equals zero, we know that the two vectors are parallel or antiparallel.
wbandersonjr said:Your way of answering is the direct way. This question is not so much about you computing a cross product as it is about you understanding that a cross product equal to zero means that the vectors are parallel. This is the concept that the question is reinforcing. You could do this by brute force, but that is time consuming and unnecessary if you understand the cross product well.
The vector 'B' is defined as a vector that is perpendicular to vector 'A' when the vector product is zero. This means that 'B' and 'A' are at a right angle to each other.
A vector 'B' can be zero when the vector product with 'A' is zero if 'B' is parallel or antiparallel to 'A'. This means that 'B' and 'A' are either pointing in the same direction or in opposite directions.
The vector product with 'A' being zero indicates that 'B' and 'A' are either parallel, antiparallel, or perpendicular to each other. This information can be useful in understanding the relationship between 'B' and 'A' in a given situation.
No, the vector 'B' must be zero when the vector product with 'A' is zero. This is because the vector product is calculated by taking the cross product of 'B' and 'A', and if the result is zero, it means that 'B' and 'A' are either parallel, antiparallel, or perpendicular to each other.
The vector 'B' is related to the vector product with 'A' being zero because 'B' is the vector that satisfies the condition of being perpendicular to 'A' when the vector product is zero. This means that 'B' is a special vector that has a unique relationship with 'A' when the vector product is zero.