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Calcmathlete
 2 years ago
Find the coordinates of the point where the vector line \(\vec{r} = (6 + \frac{7}{9}d)\vec{i} + (3 + \frac{4}{9}d)\vec{j} + (2  \frac{4}{9}d)\vec{k}\) intersects the plane 3x  7y + z = 5. I'd like an explanation or better yet, a guide through it rather than just a plain answer.
Calcmathlete
 2 years ago
Find the coordinates of the point where the vector line \(\vec{r} = (6 + \frac{7}{9}d)\vec{i} + (3 + \frac{4}{9}d)\vec{j} + (2  \frac{4}{9}d)\vec{k}\) intersects the plane 3x  7y + z = 5. I'd like an explanation or better yet, a guide through it rather than just a plain answer.

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LockeMcDonnell
 2 years ago
Best ResponseYou've already chosen the best response.0holy good luck with that!

hieuvo
 2 years ago
Best ResponseYou've already chosen the best response.1you know that: x=6+7/9d, y=3+4/9d, and z=24/9d ?

Calcmathlete
 2 years ago
Best ResponseYou've already chosen the best response.0Yes. I actually think I might have an answer since I asked this yesterday. Could you check it?

ScottB05
 2 years ago
Best ResponseYou've already chosen the best response.0I sence De Moivre's Theorum comming on here =)

Calcmathlete
 2 years ago
Best ResponseYou've already chosen the best response.0d = 54/11, so (24/11, 9/11, 46/11) Is this right?

ScottB05
 2 years ago
Best ResponseYou've already chosen the best response.0In your question you've mentioned i..... Is that i as in i, or i as in the Square root of 1???

Calcmathlete
 2 years ago
Best ResponseYou've already chosen the best response.0i as in unit vector \(\vec{i}\)

ScottB05
 2 years ago
Best ResponseYou've already chosen the best response.0Of course. Thank you :)

hieuvo
 2 years ago
Best ResponseYou've already chosen the best response.1that 7/9 or what, cant see the problem clearly

Calcmathlete
 2 years ago
Best ResponseYou've already chosen the best response.0Here's my work if it helps... \[\vec{r} = (6 + \frac{7}{9}d)\vec{i} + (3 + \frac{4}{9}d)\vec{j} + (2  \frac{4}{9}d)\vec{k}\]\[3(6 + \frac79d)  7(3 + \frac49d) + (2  \frac49d) = 5\]\[18 + \frac{21}{9}d  21  \frac{28}{9}d + 2  \frac49d = 5\]\[\frac{11}9d = 6\]\[d = 6 \times \frac9{11}\]\[d = \frac{54}{11}\]

hieuvo
 2 years ago
Best ResponseYou've already chosen the best response.1So just plug in to find coordinate. Is this cal 3?
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