Finding components vector

So, use the slope of A to find the slope of C. Then, use the dot product to find the magnitude of C.In summary, to find the x and y components of vector C⃗, you can either set up equations using the dot product and the fact that A⃗ and C⃗ are perpendicular, or use the slope of A⃗ to find the slope of C⃗ and then use the dot product to find the magnitude of C⃗.
  • #1
Kieran12
6
0

Homework Statement


You are given vectors A⃗ = 4.8 i^− 6.4 j^ and B⃗ = - 3.6 i^+ 6.8 j^. A third vector C⃗ lies in the xy-plane. Vector C⃗ is perpendicular to vector A⃗ and the scalar product of C⃗ with B⃗ is 19.0.

Find the x -component of vector C⃗ .

Find the y-component of vector C⃗ .

Homework Equations


Dot Product
Cross Product

The Attempt at a Solution


[/B]
No idea where to start on this one really. I've plotted the A and B vectors on a graph and that's about as far as I;ve got.

Cheers everyone.
 
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  • #2
For A and C to be perpendicular, their dot product must equal zero. Try setting ##C=x\hat i + y \hat j ## and satisfy the relations.
Otherwise, if you want to think in terms of lines, the perpendicular to a line with slope m has slope -1/m.
 

1. What is a components vector?

A components vector, also known as a component form vector, is a representation of a vector in terms of its horizontal and vertical components. It is used to break down a vector into its individual parts, which can then be used to calculate its magnitude and direction.

2. How do you find the components vector of a given vector?

To find the components vector of a given vector, you can use the trigonometric functions sine and cosine. The horizontal component is found by multiplying the vector's magnitude by the cosine of its angle, and the vertical component is found by multiplying the vector's magnitude by the sine of its angle.

3. Why is it important to find the components vector?

Finding the components vector is important because it allows us to analyze and understand the motion of an object in two dimensions. It also enables us to perform various calculations, such as finding the resultant vector or determining the vector's direction.

4. Can you find the components vector of a vector in three dimensions?

No, the components vector is only applicable to vectors in two dimensions. In three dimensions, vectors have three components (x, y, and z), and are represented using coordinates instead of just horizontal and vertical components.

5. Are there any real-life applications of finding components vector?

Yes, finding components vector has many real-life applications, such as in navigation, physics, and engineering. For example, it is used in calculating the forces acting on an object in two dimensions, determining the direction and magnitude of wind or ocean currents, and plotting the trajectory of a projectile.

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