- #1
sushichan
- 12
- 1
Homework Statement
(I did not copy the problem statement, but basically solve the system of equations if there is solution and give a geometrical interpretation)
P1: 2x - y + 6z = 7
P2: 3x + 4y + 3z = -8
P3: x - 2y - 4z = 9
Homework Equations
Scalar triple product: n1⋅(n2 × n3)
The Attempt at a Solution
(Step 1): Checked that they are not parallel
(Step 2): Checked that they are not coplanar
(Step 3): Find the unique solution
R2 - 3R3
⇒ 0x + 10y + 15z = -35
⇒ 6y + 9z = -21
R1 - 2R3
⇒ 0x + 3y + 14z = -11
⇒ 6y + 28z = -22
⇒ -21 - 9z = -22 - 28z
⇒ z = -1/19
⇒ y = -65/19
⇒ x = 37/19
(Edited: i double checked values for y & x)
Although the answer is that they intersect at (3, -5, 1)
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