Questions from General Calculus

Q: If a ∙ b = 3 and a × b

If a ∙ b = 3 and a × b = 1, 2, 2 , find the angle between a and b.

Q: Find the unit vectors that are parallel to the tangent line to

Find the unit vectors that are parallel to the tangent line to the parabola y − x2 at the point (2, 4).

Q: (a). Find all vectors v such that 1,

(a). Find all vectors v such that 1, 2, 1 × v = 3, 1, −5 (b). Explain why there is no vector v such that 1, 2, 1 × v = 3, 1, 5

Q: (a). Let P be a point not on the line

(a). Let P be a point not on the line L that passes through the points Q and R. Show that the distance d from the point P to the line L is (b). Use the formula in part (a) to find the distance from...

Q: Show that |a × b |2 = |a |

Show that |a × b |2 = |a |2 | b |2 - (a ∙ b)2.

Q: Find the cross product a × b and verify that it is

Find the cross product a × b and verify that it is orthogonal to both a and b. a = 1 2 i + 1 3 j + 1 4 k, b = i + 2 j – 3k

Q: Find the cross product a × b and verify that it is

Find the cross product a × b and verify that it is orthogonal to both a and b. a = t i + cos t j + sin tk, b = i - sin t j + cos tk

Q: If a = i - 2k and b = j + k

If a = i - 2k and b = j + k, find a × b. Sketch a, b, and a × b as vectors starting at the origin.

Q: Find parametric equations and symmetric equations for the line. The

Find parametric equations and symmetric equations for the line. The line through (-6, 2, 3) and parallel to the line 1 2 x – 1 3 y = z + 1

Q: The figure shows a curve C given by a vector function r

The figure shows a curve C given by a vector function r (t). (a). Draw the vectors r (4.5) – r (4) and r (4.2) – r (4). (b). Draw the vectors (c). Write expressio...