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Two sloping steel plates in a bridge frame lie in the… | StemPy Lab
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Two sloping steel plates in a bridge frame lie in the planes x + 2y - z = 1 and 2x - y + z = 3. Where they meet, a weld seam runs along a straight line. A welder needs a vector that points along the seam. Which vector does she use?
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Vectors and Three-Dimensional Geometry › Three-Dimensional Geometry
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Two sloping steel plates in a bridge frame lie in the planes
x
+
2
y
−
z
=
1
x + 2y - z = 1
x
+
2
y
−
z
=
1
and
2
x
−
y
+
z
=
3
2x - y + z = 3
2
x
−
y
+
z
=
3
. Where they meet, a weld seam runs along a straight line. A welder needs a vector that points along the seam. Which vector does she use?
i
^
−
3
j
^
−
5
k
^
\hat{i} - 3\hat{j} - 5\hat{k}
i
^
−
3
j
^
−
5
k
^
i
^
+
3
j
^
+
5
k
^
\hat{i} + 3\hat{j} + 5\hat{k}
i
^
+
3
j
^
+
5
k
^
i
^
+
2
j
^
−
k
^
\hat{i} + 2\hat{j} - \hat{k}
i
^
+
2
j
^
−
k
^
3
i
^
+
j
^
3\hat{i} + \hat{j}
3
i
^
+
j
^
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← Two parallel glass sheets lie in the planes 2x - y + 2z = 1 and 4x - 2y + 4z = -10, with lengths in metres. What is the distance between the sheets?
The figure shows the part of a plane in the first octant. It meets the axes at A(6, 0, 0), B(0, 3, 0) and C(0, 0, 2), with lengths in metres. What is the shortest distance from the origin to the plane? →
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