Final answer:
The answer is true; if w is a subset of v that is also a vector space, then w is a subspace of v. The addition of five vectors does not necessarily result in a greater magnitude compared to the addition of two vectors, and knowing only the angles of two vectors is not enough to find the angle of their resultant vector.
Step-by-step explanation:
If v is a vector space and w is a subset of v that is also a vector space, then w is a subspace of v. The answer to this statement is true. A subspace is defined as a subset of a vector space that is itself a vector space under the same addition and scalar multiplication. Hence, if w satisfies all the requirements of a vector space within the context of v, it is indeed a subspace of v. For question 81 regarding the addition of five vectors, it is not necessarily true that their addition always results in a vector with a greater magnitude compared to the addition of any two of the vectors. Vector addition is commutative, but the resultant vector's magnitude depends on the directions and magnitudes of the individual vectors. In some cases, the addition of multiple vectors could result in cancellation effects if the vectors have opposing directions. Regarding question 83, it is false that if only the angles of two vectors are known, we can find the angle of their resultant addition vector. Knowing only the angles is insufficient; we also need information about the magnitudes of the vectors to determine the resultant vector's angle. For question 60, it is true that a vector can form the shape of a right angle triangle with its x and y components. This is often visualized in a coordinate space where the vector's components represent the legs of the triangle, and the vector itself represents the hypotenuse.