Question

In: Advanced Math

Find the intersection point (if any) of the lines r1(t)=(17,54,−22)+t(−3,−8,3)r1(t)=(17,54,−22)+t(−3,−8,3) and r2(s)=(−67,−50,37)+s(12,8,−7)r2(s)=(−67,−50,37)+s(12,8,−7). Please show full working/steps...

Find the intersection point (if any) of the lines r1(t)=(17,54,−22)+t(−3,−8,3)r1(t)=(17,54,−22)+t(−3,−8,3) and r2(s)=(−67,−50,37)+s(12,8,−7)r2(s)=(−67,−50,37)+s(12,8,−7).

Please show full working/steps to help with learning

Expert Solution

Solution:

Given Lines are

and

first we write both as

Now, to find intersecting point equate the components of both lines

we have

So we have system of linear equations.

Now we solve them by using matrix method:

so its matrix representation is

applying

By using values of in , we get

Here, is the common point of .

Hence, it is the required intersecting point.

This complete the solution.

Colby Messinger answered 3 years ago

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