1. Example-1
1. Find isCoplanar(A,B,C)
`A=(1,2,3)`,`B=(2,4,6)`,`C=(3,4,5)`
Solution:
Here `vec A=(1,2,3),vec B=(2,4,6),vec C=(3,4,5)`
The 3 vectors are coplanar, if their scalar triple product is zero
1. Calculate scalar triple product
`A*(B xx C)`
`=|[A_1,A_2,A_3],[B_1,B_2,B_3],[C_1,C_2,C_3]|`
`=|[1,2,3],[2,4,6],[3,4,5]|`
`=1(4xx5-6xx4)-2(2xx5-6xx3)+3(2xx4-4xx3)`
`=1(20-24)-2(10-18)+3(8-12)`
`=1(-4)-2(-8)+3(-4)`
`=-4+16-12`
`=0`
Here scalar triple product is zero, so vectors are coplanar
2. Find isCoplanar(A,B,C)
`A=(5,-1,1)`,`B=(-2,3,4)`,`C=(3,4,5)`
Solution:
Here `vec A=(5,-1,1),vec B=(-2,3,4),vec C=(3,4,5)`
The 3 vectors are coplanar, if their scalar triple product is zero
1. Calculate scalar triple product
`A*(B xx C)`
`=|[A_1,A_2,A_3],[B_1,B_2,B_3],[C_1,C_2,C_3]|`
`=|[5,-1,1],[-2,3,4],[3,4,5]|`
`=5(3xx5-4xx4)--1((-2)xx5-4xx3)+1((-2)xx4-3xx3)`
`=5(15-16)--1(-10-12)+1(-8-9)`
`=5(-1)--1(-22)+1(-17)`
`=-5-22-17`
`=-44``!=0`
Here scalar triple product is not zero, so vectors are not coplanar
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
|
