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# C4 Vector Geometry help watch

1. Question:
2 intersecting lines have the equation r_1 = (2,9,13) +s(1,2,3) and r_2 = (λ, 7,-2) + t(-1,2,-3). Find λ.

What I did was equate the x and z values of the lines and do simultaneous equations to eliminate the other variables. So i.e:

x: s+t = λ -2 (1) (then multiplied by 3)
z: 3s + 3t = -15 (2)

The answer I got was λ = -3. But the back of the book says -6. Can someone spot where I'm going wrong please? Is this even the right approach to take?

Thank you.
2. (Original post by HotCoco.)
Question:
2 intersecting lines have the equation r_1 = (2,9,13) +s(1,2,3) and r_2 = (λ, 7,-2) + t(-1,2,-3). Find λ.

What I did was equate the x and z values of the lines and do simultaneous equations to eliminate the other variables. So i.e:

x: s+t = λ -2 (1) (then multiplied by 3)
z: 3s + 3t = -15 (2)

The answer I got was λ = -3. But the back of the book says -6. Can someone spot where I'm going wrong please? Is this even the right approach to take?

Thank you.
I also get lambda as - 3

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