How Do You Determine the Components of a Vector Perpendicular to Another?

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To determine the components of vector C that is perpendicular to vector A and has a scalar product of 19.0 with vector B, the dot product of A and C must equal zero. This means that if C is expressed as C = x i + y j, the equation 4.8x - 6.4y = 0 must be satisfied. Additionally, the scalar product condition requires that -3.6x + 6.8y = 19.0. Solving these two equations simultaneously will yield the x and y components of vector C. This approach combines the properties of dot products and the geometric interpretation of perpendicular vectors.
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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


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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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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.
 
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