3. Vectors

Find the magnitude and direction of the vector C =2B × A.

(I) Show that (b) î x ĵ, = k̂ , î x k̂ , = - ĵ , and ĵ x k̂ = î .

(I) If vector A→ points along the negative x axis and vector B→ along the positive z axis, what is the direction of (a) A→ x B→ and (b) B→ x A→? (c) What is the magnitude of A→ x B→ and B→ x A→?

(I) The directions of vectors A → and B→ are given below for several cases. For each case, state the direction of A→ x B→ . (d) A→ points straight up, B→ points straight down.

(II) Determine (a) the vector product A→ x B→ and (b) the angle between A→ and B→ if A→ = 7.4î - 3.5ĵ and B→ = -8.5î + 4.6ĵ + 2.0k̂ . [Hint: To resolve an ambiguity, the dot product may prove useful.]