Give parametric equations for the line a through 2 24 35

Give parametric equations for the line . . .

a) through (2, 2.4, 3.5) and parallel to the vector 3i + 2 j ? k.

b) through the point (2, 4, 6) and perpendicular to the plane x ? y + 3z = 7

Show full work please

Solution

a)

through (2, 2.4, 3.5) and parallel to the vector 3i + 2 j ? k.

<2 , 2.4 , 3.5> + t<3 , 2 , -1>

<2 , 2.4 , 3.5> + <3t , 2t , -t>

<2 + 3t , 2.4 + 2t , 3.5 - t> ----> ANSWER

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b) through the point (2, 4, 6) and perpendicular to the plane x ? y + 3z = 7

(2 , 4 , 6> + t(1 , -1 , 3>

<2 , 4 , 6> + <t , -t , 3t>

<2 + t , 4 - t , 6 + 3t> ---> ANSWER