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Vector parallel to the lineHi Guys! I was doing a vector math problem and I got stuck on how to find the vector parallel to the line. The question is : Determine if the plane given by -x+2z=10 and the line given by r=(5,2-t,10+4t) are orthogonal, parallel or neither. Now I have already found the normal vector as the first step, but also I have to find the vector that is parallel to the line so as that I can cross it with the normal vector to prove if it they are parallel to each other. Thank you. |

Is there a point that lies in the given plane and on the given line? |

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In general, a vector in the direction of the line $\displaystyle x= x_0+ At$, $\displaystyle y= y_0+ Bt$, $\displaystyle z= z_0+ Ct$ is <A, B, C>. |

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#Slumerican |

A tad faster might be: A normal to plane is (-1,0,2) by inspection. Line is r=(5,2,10)+t(0,-1,4) (-1,0,2)x(0,-1,4)=0 [Note by moderator: (-1, 0, 2) × (0, -1, 4) = (2, 4, 1)] |

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