Thomas Calculus 13th [Solutions]

900 Chapter 12 Vectors and the Geometry of Space
18. The direction PQ 3i 2j and P(0, 2, 0)
x 3 t, y 2 2 t, z 0, where 0 t 1
19. The direction PQ 2i 2j 2k and P(2, 0, 2)
x 2 2 t, y 2 t, z 2 2 t , where 0 t 1
20. The direction PQ i 3j k and P(1, 0, 1)
x 1 t, y 3 t, z 1 t , where 0 t 1
21. 3( x 0) ( 2)( y 2) ( 1)( z 1) 0 3x 2y z 3
22. 3( x 1) (1)( y 1) (1)( z 3) 0 3x y z 5
i j k
23. PQ i j 3 k, PS i 3j 2k PQ PS 1 1 3 7i 5j 4k is normal to the plane
1 3 2
7( x 2) ( 5)( y 0) ( 4)( z 2) 0 7x 5y 4z
6
i j k
24. PQ i j 2 k, PS 3i 2j 3k PQ PS 1 1 2 i 3j k is normal to the plane
3 2 3
( 1)( x 1) ( 3)( y 5) (1)( z 7) 0 x 3y z 9
25. n i 3j 4 k, P(2, 4, 5) (1)( x 2) (3)( y 4) (4)( z 5) 0 x 3y 4z
34
26. n i 2 j k,
P(1, 2, 1) (1)( x 1) ( 2)( y 2) (1)( z 1) 0 x 2y z 6
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