Question

Which of the above statements is or are correct:
A. Two non-zero, non-collinear vectors are linearly independent.
B. Any three coplanar vectors are linearly dependent.

Answer 1

Hint: Here the given question needs to find the correctness of the given statement which is about the vector plane, here we need to find the related properties of the given statement in order to check the correctness of the statements.

Complete step by step answer:
Here we are given with to statements where we have to see that the given statements are correct or not, here we will see both the statements separately and then check for the related properties or arguments which prove the statement is correct or false, on solving we get:
The first statement is that two non-zero, non-collinear vectors are linearly independent, and this statement is correct since non-collinear vectors will never collide and hence do not have any possible solution, hence are independent of each other.
The second statement is that any three coplanar vectors are linearly dependent, here we know when the vectors are coplanar then they lies on the same plane hence it is sure that they will collide somewhere in the plane, and the point of intersection will give the possible solution for the intersection, hence the vectors will be dependent on each other, therefore the given statement is also correct.
Here we see that both the given statements are correct.

Note: Here in the assertion type of question we have to check with the given argument for the correctness of the statements, and as here we can see that both the statements given justify their statements hence are correct.