For the two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ in the figure$1.39$, find the magnitude and direction of the vector product $\overrightarrow{A}\times \overrightarrow{B}$.

Evaluate the cross products and A ✕ B and C ✕ D.

Vector A ＝ 3î＋ĵ and vector B＝ 3î - 2ĵ ＋ 2k. What is the cross product A ✕ B?

Show that  î x ĵ = k̂ , î x k̂ = - ĵ, and ĵ x k̂ = î.

(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.]

If vector $\vec{A}$ points along the negative $x$ axis and vector $\vec{B}$ along the positive $z$ axis, what is the direction of (a) $\vec{A}\times \vec{B}$ and (b) $\vec{B}\times \vec{A}$? (c) What is the magnitude of $\vec{A}\times \vec{B}$ and $\vec{B}\times \vec{A}$?

(I) The directions of vectors $\vec{A}$ and $\vec{B}$ are given below for several cases. For each case, state the direction of $\vec{A}\times \vec{B}$. $\vec{A}$ points straight up, $\vec{B}$ points straight down.