Question

Which of the following statements are true about vectors u and v shown below? (There may be multiple correct answers.)

Group of Answer Choices:
A. u and v are orthogonal.
B. The dot product of u and v is zero.
C. u and v are parallel.
D. u and v span all of R^n.

Answer 1

If vectors u and v are orthogonal, statements A and B about them being orthogonal and their dot product being zero are correct . Statement C is incorrect for orthogonal vectors, and D requires additional information to verify.

Step-by-step explanation:

When two vectors u and v are <orthogonal, their dot product is zero, this is due to the cosine of the angle between them being zero (cos 90° = 0). Hence, if vectors u and v are orthogonal, statement A is correct, and so is statement B since their dot product equals zero. Statement C would be incorrect if the vectors are orthogonal, as parallel vectors have either the same or exactly opposite direction but with a different angle than 90°.


Statement D requires further information; two vectors span all of Rⁿ if and only if they are linearly independent and not scalar multiples of each other. However, for n > 2, two vectors cannot span all of Rⁿ, as you would need at least n linearly independent vectors to span an n-dimensional space.