Question

a, b, c are non-coplanar vectors. Prove that the following four points are coplanar.
-a + 4b - 3c, 3a + 2b - 5c, - 3a + 8b - 5c, -3a + 2b + c.
(ii) 6a + 2b - C, 2a - b + 3c, - a + 2b - 4c, -12a - b - 3c.
directions of the coordinate gyes then show​

Answer 1

Step-by-step explanation:

Given A, b, c are non-coplanar vectors. Prove that the following four points are coplanar.

• Let P = - a + 4b – 3c
•       Q = 3a + 2b – 5c
•       R = - 3a + 8b – 5c
•      S = - 3a + 2b + c
• Now we need to find the vectors. So we have
• PQ = 4a – 2b – 2c
• QR = - 6a + 6b + 0c
• RS = 0a – 6b + 6c
• So now we need to find the determinant, so we get
•                        4          - 2          - 6
•                      -6            6             0
•                       0           - 6            6
• So we have
•            4 (36 + 0) – (-2) (-36 – 0) – 2 (36 – 0)
•                  144 + 2(-36) – 2(36)
•                  144 – 72 – 72
•                           0
• So we have proved that the points PQ, QR and RS are coplanar.
• Then vector P,Q,R,S points are also coplanar.

Reference link will be

https://brainly.in/question/6583509

Answer 2

Answer:

Step-by-step explanation: