Chapter 1: Vectors, Lines and Planes
Section 1.3: Dot Product
In the xy-plane, obtain all vectors that are orthogonal to A=3 i+2 j.
If B=u i +v j is orthogonal to A=3 i+2 j, then A·B=3 u+2 v=0 must hold. Solving this equation for, say, v=−3 u/2 gives
B=uv=u−3 u/2=u1−3/2=2 λ1−3/2=λ2−3
The vector B can be any multiple of 2 i−3 j.
Enter A as per Table 1.1.1.
Context Panel: Assign Name
Enter B as per Table 1.1.1.
Determine v=vu from the equation A·B=0
Common Symbols palette: Dot-product operator
Set the dot product of A and B equal to zero.
Context Panel: Solve≻Isolate Expression for≻v
Context Panel: Substitute Into≻B
Context Panel: Evaluate at a Point≻u = 2*lambda
→isolate for v
→evaluate at point
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