Vectors 20.5

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Last updated 12:03 PM on 4/4/26
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9 Terms

1
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Show that the lines intersect and solve r = (1,0, 3) + u(2, 1, 1) and r = (2, -1, -1) + t(-5, -1, 2)

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2
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Show that r = (1, 0, 3) + t(2, 1, 1) and r (3, 1, 4) + u(4, 2, 2) are coincident lines

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3
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Show that r = (1, 0, 3) + r(2, 1, 1) and r = (2, -1, -1) + t(-5, -1, 3) are skew lines

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4
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What is a dot (axb)

Answer : 0 (scalar) NOT a dot a x a dot b

5
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If (1, -1, 4) is perpendicular to normal of plane 1 and 3 then…

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6
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What happens if line lies on plane AND line not parallel to plane

  1. Line lies on plane → parallel to plan, line perpendicular to plane

  2. Line not parallel to plane → intersect at 1 point

7
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8
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Show that the line r = (2, 1, -1) + t(3, 1, 3) is parallel to the plane r dot (-1, 0, 1) = 1

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9
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Find the equation of the line of interesection of the planes r (7, 2, -3) = 4 and r (2, 1, 0) = 5

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