Find a vector equation for die line through die point ? = (0. 3. 5) and parallel

Question

Find a vector equation for die line through die point ? = (0. 3. 5) and parallel to the vector mathbf{v} = langle {-2,3,4} angle. Note: there are many correct answers to this question, so in order for WebWork to check your answer, you need to find the particular vector equation that has mathbf{r}(0)=? and mathbf{v} as the direction vector of the line. Use the variable t as the parameter. This amounts to sohing the problem in the standard way. mathbf{r}(t) = mathbf{i} + mathbf{j} + mathbf{k} Rewrite this in terms of the parametric equations for the line, x = y = z =

Explanation / Answer

parametric equation to the line passing though (0,3,5) and parellel to <-2,3,4>

(x-0)/(-2)=(y-3)/3=(z-5)/4=t

then x=-2t; y=3t+3; z=4t+5

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