Smart Solution
What is the distance from
E to the plane BPQ?
(a few seconds only)
Musical
English Subtitle
Distance between
point and plane
“
Leonardo Sembiring
leonardo.sembiring@gmail.com
PLEASE DO NOT TRY IT AT HOME
BASIC CONCEPT IS PRECIOUS THING
JUST DO IT AT EXAM
How to determine the coordinates from origin? Please use the following rules.
X+
X-
Z+
Z-
Y+
Y-
UNDER
LEFT
ABOVE
BACK
FRONT
RIGHT
3
1
2
1
Assuming one point in the plane as origin with coordinate (0, 0, 0)
2
Find coordinates of two other points in the plane and point outside of plane
0
2
2
2
-1
+2
+2
+1
(0, 0, 0)
-2
0
-2
+2
Length of sides of the cube is 2.
P and Q are midpoints of line segment EA and GH respectively.
What is the distance from
point E to the plane BPQ?
+
2
-1
2
2
-2
0
1
-1
2
2
-2
0
1
2
-3
4
-2
0
2
4
9
16
-4
0
8
B (0, 0, 0)
P
Q
E
4
29
Distance =
=
4
29
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3
Copy coordinates of plane to the right and determine plane vector
4
Square the plane vector and sum products of both vectors
5
Find the distance
plane vector
point vector
2.1-2.0 = 2
(-1).0-2.(-2) = 4
2.(-2)-(-1).1 = -3
1
2
3
square
multiply
add up
SMART IDEAS FOR SOLVING MATHEMATICS
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CREDITS
-1
2
2
-1
2
2
-2
0
1
-2
0
1
2
-3
4
-2
2
2
4
9
16
-4
-6
8