Plane through a point (or containing a line) parallel to two given lines or vectors
This type of question, asked 5 times: 4 May 2023 S2, 10 May 2023 S2, 16 May 2023 S2, 11 Apr 2026 S2, 19 May 2026 S1. All 6 questions below, oldest first.
Try each one first, then open its answer.
Question 1
4 May 2023 S2
110
The equation of the plane, passing through the point (−1,2,−3) and parallel to the lines 3x−1=2y−2=−4z and 2x=−3y−1=2z−2, is
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Question 2
10 May 2023 S2
134
The equation of the plane through the point (2,−1,−3) and parallel to the lines 3x−1=2y+2=−4z and 2x=−3y−1=2z−2 is
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Question 3
10 May 2023 S2
102
The vector equation of the plane passing through the point A(1, 2, -1) and parallel to the vectors 2i^+j^−k^ and i^−j^+3k^ is
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Question 4
16 May 2023 S2
139
The equation of plane through the point (2,−1,−3) and parallel to lines 3x−1=2y+2=−4z and 2x=−3y−1=2z−2 is
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Question 5
11 Apr 2026 S2
92
The vector equation of the plane passing through the point A(−2,7,5) and parallel to the vectors 4i^−j^+3k^ and i^+j^+k^ is ...
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Question 6
19 May 2026 S1
95
The equation of the plane containing the line 4x+1=−1y−2=3z+5 and parallel to the vector i^+j^−k^ is ax+by+cz=9. Then, the value of a+b−c is:
