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Proving two vectors are coplanar and finding the Cartesian equation of the plane whic

Show that r = 3i+2j+k+t(-i+2j+k) and r=3i+9j+2k+t(2i+3j-k) are coplanar and finding the Cartesian equation of the plane which contains them.

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Reply 1

SpanishTashman

Original post by SpanishTashman

Show that r = 3i+2j+k+t(-i+2j+k) and r=3i+9j+2k+t(2i+3j-k) are coplanar and finding the Cartesian equation of the plane which contains them.

Posted from TSR Mobile

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Reply 2

TeeEm

Original post by SpanishTashman

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crossing their direction vectors and dotting the answer with any of the 2 direction vectors should give you zero if coplanar

Reply 3

SpanishTashman

Okay I've crossed the direction vectors and got -5i+j-7k, how would I go about dotting that? As in which vectors represents a and n?

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Reply 4

SpanishTashman

Original post by TeeEm

crossing their direction vectors and dotting the answer with any of the 2 direction vectors should give you zero if coplanar

Okay I've crossed the direction vectors and got -5i+j-7k, how would I go about dotting that? As in which vectors represents a and n?

Posted from TSR Mobile

Reply 5

TeeEm

Original post by SpanishTashman

Okay I've crossed the direction vectors and got -5i+j-7k, how would I go about dotting that? As in which vectors represents a and n?

Posted from TSR Mobile

Ok

bit busy here

if the lines intersect then they are Coplanar since they are not parallel

So find intersection

the cross product of their direction then is the normal of the plane they define

use the intersection point and the normal to find plane