Which of the following are the direction ratios of S?
Direction: Consider the following for the two (02) items that follow :<br>Let S be the line of intersection of two planes x+y+z=1 and 2x+3y-4z=8.
- A. \langle -7, -6, 1 \rangle
- B. \langle -7, 6, 1 \rangle ✓
- C. \langle -6, 5, 1 \rangle
- D. \langle 6, 5, 1 \rangle
Correct Answer: B. \langle -7, 6, 1 \rangle
Explanation
The direction ratios of the line of intersection S are proportional to the cross product of the normal vectors of the two planes. The normals are \vec{n_1} = \langle 1, 1, 1 \rangle and \vec{n_2} = \langle 2, 3, -4 \rangle. The cross product is \vec{n_1} \times \vec{n_2} = \langle 1(-4) - 1(3), 1(2) - 1(-4), 1(3) - 1(2) \rangle = \langle -7, 6, 1 \rangle.
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