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Math  /  Geometry

QuestionGive a vector parametric equation for the line through the point (4,5,5)(4,5,5) that is parallel to the line ⟨−2,−4−4t,5+5t⟩\langle-2,-4-4 t, 5+5 t\rangle : L(t)=L(t)= □\square Preview Mv Answers Submit Answere

Studdy Solution

STEP 1

1. The line is represented in vector parametric form.
2. The line passes through the point (4,5,5)(4, 5, 5).
3. The line is parallel to the given line ⟨−2,−4−4t,5+5t⟩\langle -2, -4 - 4t, 5 + 5t \rangle.

STEP 2

1. Identify the direction vector of the given line.
2. Use the point and direction vector to write the parametric equation of the new line.

STEP 3

Identify the direction vector of the given line:
The given line is in the form ⟨x0,y0+at,z0+bt⟩\langle x_0, y_0 + at, z_0 + bt \rangle, where the direction vector is ⟨0,−4,5⟩\langle 0, -4, 5 \rangle.

STEP 4

Use the point (4,5,5)(4, 5, 5) and the direction vector ⟨0,−4,5⟩\langle 0, -4, 5 \rangle to write the parametric equation of the new line:
The vector parametric equation for the line is given by:
L(t)=⟨4,5,5⟩+t⟨0,−4,5⟩ L(t) = \langle 4, 5, 5 \rangle + t \langle 0, -4, 5 \rangle
The vector parametric equation for the line is:
L(t)=⟨4,5−4t,5+5t⟩ L(t) = \langle 4, 5 - 4t, 5 + 5t \rangle

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