Vectors b and c Parallel? Find Scalar s or N for No

In summary, parallel vectors are two or more vectors that have the same direction or are in the same line, but may have different magnitudes or lengths. To determine if two vectors are parallel, you can use the dot product or compare their direction components. A scalar is a quantity that has magnitude but no direction and can be used to change the magnitude of a vector or determine the parallel relationship between two vectors. Parallel vectors can have different magnitudes, and to find the scalar or N for non-parallel vectors, the cross product can be used to find a third vector that is perpendicular to the original two. The magnitude of this third vector can then be used to determine the scalar or N for the non-parallel vectors.
  • #1
tarheels88
8
0

Homework Statement


Given vectors b and c are they parallel? If so find such scalar s that c=sb, otherwise write N for no.

a) b=<0,3,4>, c=<0,6,-8)

b) b=<10,6>, c=<-15,-9>

Homework Equations



c=sb is a property of the dot product.

The Attempt at a Solution


For a) I put No because <0,6,-8> does not = <0s, 3s, 4s> because S=2
For b) I put Yes because S=-3/2 which would give you both outcomes of the vectors

Am I correct?
 
Physics news on Phys.org
  • #2
Yes, you are. If you'd explain why you need to pick s=2 in the first case, that would probably help. "because s=2" isn't much of an explanation.
 
  • #3
I put s=2 because I was finding a multiple of the two vectors given. Then I calculate 3s=6, that would then calculate to c=2.
 
  • #4
tarheels88 said:
I put s=2 because I was finding a multiple of the two vectors given. Then I calculate 3s=6, that would then calculate to c=2.

Right, so the only possibility is s=2, and since that doesn't work there is no s that works. I knew you knew that. Just wanted you to add that if you are turning this in as a homework exercise.
 

FAQ: Vectors b and c Parallel? Find Scalar s or N for No

What is the definition of parallel vectors?

Parallel vectors are two or more vectors that have the same direction or are in the same line, but may have different magnitudes or lengths.

How do you determine if two vectors are parallel?

To determine if two vectors are parallel, you can use the dot product. If the dot product of two vectors is equal to the product of their magnitudes, then they are parallel. Another way is to compare the direction components of the two vectors. If they are proportional, then the vectors are parallel.

What is a scalar in relation to parallel vectors?

A scalar is a quantity that has magnitude but no direction. In the context of parallel vectors, a scalar can be used to multiply or divide a vector to change its magnitude without changing its direction. It can also be used to determine if two vectors are parallel.

Can parallel vectors have different magnitudes?

Yes, parallel vectors can have different magnitudes. The only requirement for parallel vectors is that they have the same direction or are in the same line. Magnitude does not affect the parallel relationship between vectors.

How do you find the scalar or N for non-parallel vectors?

To find the scalar or N for non-parallel vectors, you can use the cross product. The cross product of two vectors will give you a third vector that is perpendicular to the original two. The magnitude of this third vector can be used to find the scalar or N for the non-parallel vectors.

Similar threads

Finding Non-Trivial Solution(s) For 3x3 Matrix
Replies
9
Views
897
Covariance of partitioned linear combination
Replies
3
Views
1K
Vector Form: Line Passing Through (2, -1) and Parallel to 2x-3y=1
Replies
11
Views
2K
Vector Equation of Plane w/ (-2,2,1) & Parallels (1,1,2) and (2,1,-1)
Replies
1
Views
883
Let A, B, and C be vectors in R3....prove r lies in a plane
Replies
6
Views
1K
Vector Subspace: Show S is a Subspace, Determine Basis & Find Dimension
Replies
2
Views
1K
Vector Algebra: Finding a parallel vector
Replies
7
Views
2K
Finding a vector using scalar and vector projections
Replies
3
Views
2K
Find parametric equation at point, and parallel to planes?
Replies
5
Views
2K
Coefficients in the expansion of (1+x)n in A.P, find n
Replies
6
Views
1K

Hot Threads

Recent Insights

Back
Top