Homework help

The numbers in brackets are supposed to be in subscript so V(2) would be V subscript 2 and the number in front is just multiply, all the variables are vectors so they have a arrow on top.

Determine if,
W(1) = 2V(1) + 3V(2) , W(2) = V(2) + 2V(3) and W(3) = -V(1) - 3V(3) are coplanar

Please help

Without any recent related training, I see the problem one you can visualize in 3D.
Vectors V(1) and V(2) may define a plane, and any linear combination of the two, like W(1) is in that plane, so W(1), V(1) and V(2) are coplanar.
By the same reasoning
W(2) is coplanar with V(2) and V(3), and
W(3) is coplanar with V(1) and V(3).

The problem is, there is not enough information.
if V(3) is in the same plane as V(1) and V(2), all the vectors involved are coplanar;
if V(3) is not the same plane as V(1) and V(2), then W(1), W(2), and W(3) are not coplanar.

Originally Posted by Tess213

The numbers in brackets are supposed to be in subscript so V(2) would be V subscript 2 and the number in front is just multiply, all the variables are vectors so they have a arrow on top.

Determine if,
W(1) = 2V(1) + 3V(2) , W(2) = V(2) + 2V(3) and W(3) = -V(1) - 3V(3) are coplanar

Please help

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