vector equation problem ( Please help me)

[Jay007]

Find point d on the line of r(t)=(0,0,0)+(−1,1,1)t
which make the triangular pyramid abcd has the volume of 4 unit cube when a(0,0,0),b(1,0,1),c(0,1,0) are the points on the plane of −x+z=0.

 

[Deleted member 4993]

View attachment 21343



Find point d on the line of r(t)=(0,0,0)+(−1,1,1)t
which make the triangular pyramid abcd has the volume of 4 unit cube when a(0,0,0),b(1,0,1),c(0,1,0) are the points on the plane of −x+z=0.

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[Dr.Peterson]

View attachment 21343
Find point d on the line of r(t)=(0,0,0)+(−1,1,1)t
which make the triangular pyramid abcd has the volume of 4 unit cube when a(0,0,0),b(1,0,1),c(0,1,0) are the points on the plane of −x+z=0.

This looks like a job for the scalar triple product. Are you familiar with that? Give it a try, and show us what you find.