Questions from General Calculus

Q: Find the angle between the vectors. (First find an exact

Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.) a = −2, 5 , b = 5, 12

Q: Find the angle between the vectors. (First find an exact

Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.) a = 1, −4, 1 , b = 0, 2, −2

Q: Find the angle between the vectors. (First find an exact

Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.) a = −1, 3, 4 , b = 5, 2, 1

Q: What is the angle between the given vector and the positive direction

What is the angle between the given vector and the positive direction of the x-axis? i + 3 j

Q: Find the angle between the vectors. (First find an exact

Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.) a = 4i - 3j + k, b = 2i - k

Q: Find a ∙ b. a = 5, −

Find a ∙ b. a = 5, −2 , b = 3, 4

Q: Find the angle between the vectors. (First find an exact

Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.) a = 8i - j + 4k, b = 4j + 2k

Q: Find, correct to the nearest degree, the three angles of

Find, correct to the nearest degree, the three angles of the triangle with the given vertices. P (2, 0), Q (0, 3), R (3, 4)

Q: Use vectors to decide whether the triangle with vertices P (1

Use vectors to decide whether the triangle with vertices P (1, -3, -2), Q (2, 0, -4), and R (6, -2, -5) is right-angled.

Q: Find a unit vector that is orthogonal to both i + j

Find a unit vector that is orthogonal to both i + j and i + k.