Find the value of x such that the points A(3, 2, 1), B(4, x, 5), C(4, 2, −2) and D(6, 5, −1) are coplanar. A. 5 B. 3 C. 1 D. −1 Answer: A) 5 Explanation: Vectors AB = î + (x−2)ĵ + 4k̂, AC = î + 0ĵ − 3k̂, AD = 3î + 3ĵ − 2k̂. Coplanar means [AB AC AD] = 0. Det: 1(0 − (−9)) − (x−2)(−2 − (−9)) + 4(3 − 0) = 0. 9 − 7(x−2) + 12 = 0. 21 = 7(x−2). x−2 = 3 → x = 5.

imo class 12 vector algebra

Find the value of x such that the points A(3, 2, 1), B(4, x, 5), C(4, 2, −2) and D(6, 5, −1) are coplanar.

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#IMO #Class 12 #Mathematics #Vector Algebra #achievers

Find the value of x such that the points A(3, 2, 1), B(4, x, 5), C(4, 2, −2) and D(6, 5, −1) are coplanar.

A. 5
B. 3
C. 1
D. −1

Answer: A) 5

Explanation: Vectors AB = î + (x−2)ĵ + 4k̂, AC = î + 0ĵ − 3k̂, AD = 3î + 3ĵ − 2k̂. Coplanar means [AB AC AD] = 0. Det: 1(0 − (−9)) − (x−2)(−2 − (−9)) + 4(3 − 0) = 0. 9 − 7(x−2) + 12 = 0. 21 = 7(x−2). x−2 = 3 → x = 5.

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