Determine whether the vectors are parallel, perpendicular or neither.
1) v = (4,1), w = (1,-4)
2) v = (2,3), w = (4,6)
3) v = (2,3), w = (3,-3)
Please and thanks!
to be perpendicular, the dot product must be zero
to be parallel, one must a scalar multiple of the other.
The question is very easy.
I don't understand how to fnd it though Reiny :( perhaps you could help?
To determine whether the vectors are parallel, perpendicular, or neither, we will use the dot product.
1) v = (4,1), w = (1,-4)
To find the dot product of two vectors u = (a, b) and v = (c, d), we use the formula: u ∙ v = ac + bd.
In this case, v ∙ w = (4)(1) + (1)(-4) = 4 - 4 = 0.
Since the dot product is zero, the vectors v and w are perpendicular.
2) v = (2,3), w = (4,6)
v ∙ w = (2)(4) + (3)(6) = 8 + 18 = 26.
Since the dot product is not zero, the vectors v and w are neither parallel nor perpendicular.
3) v = (2,3), w = (3,-3)
v ∙ w = (2)(3) + (3)(-3) = 6 - 9 = -3.
Since the dot product is not zero, the vectors v and w are neither parallel nor perpendicular.
Therefore, to summarize:
1) The vectors v = (4,1) and w = (1,-4) are perpendicular.
2) The vectors v = (2,3) and w = (4,6) are neither parallel nor perpendicular.
3) The vectors v = (2,3) and w = (3,-3) are neither parallel nor perpendicular.