Vectors: operations, dot product and angles

Question 1 of 10

Find a·b if a = (−5, 0) and b = (−1, 5).

Question 2 of 10

Given that a = (3, 4) and b = (5, −12), find (a) |a| and |b|, (b) a·b, (c) the angle between a and b to the nearest degree.

Question 3 of 10

(3, 2)·(4, 2) = ___

Question 4 of 10

Find k if the vectors (k, 12) and (3, −1) are perpendicular.

Question 5 of 10

(3, 1)·(1, 3) = ___

Question 6 of 10

(3, 5)·(4, 1) = ___

Question 7 of 10

A scalar multiple of a vector is parallel to it.

Question 8 of 10

Use vectors to prove that the diagonals of a rhombus are perpendicular.

Question 9 of 10

The zero vector has magnitude 0.

Question 10 of 10

Find a + 2b if a = (−1, 2) and b = (5, −3).