Drain Brain said:I wonder how my book did the calculation for this example
$\vec{r}=<5,2-t,10+4t>$ the vector parallel to it is $\vec{a}=<0,-1,4>$
can you show the workings of this example! TIA!
A vector is a mathematical object that has both magnitude (size) and direction. It is usually represented by an arrow pointing in the direction of the vector with a length proportional to its magnitude.
To determine if two vectors are parallel, you can use the dot product. If the dot product of two vectors is equal to zero, then they are perpendicular and not parallel. If the dot product is equal to the product of their magnitudes, then they are parallel.
Yes, a vector can be parallel to itself. This means that the vector has the same direction as itself and can have any magnitude. It is not necessary for a vector to have a different direction to be parallel to another vector.
To find a vector parallel to another vector, you can multiply the vector by a scalar (a number). This will change the magnitude of the vector but not its direction, resulting in a parallel vector.
Yes, there are infinitely many vectors that can be parallel to another vector. This is because any vector that is a scalar multiple of another vector will be parallel to it. Therefore, there can be an infinite number of vectors with different magnitudes that are parallel to a given vector.