3. Vectors

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 $\vec{B}\times \vec{A}$?

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

Given the vectors $i+j$ and $i-j$, what is the result of their cross product $\times$ using the properties of cross products (not determinants)?

Determine (a) the vector product $\vec{A}\times \vec{B}$ and (b) the angle between $\vec{A}$ and $\vec{B}$ if $\vec{A}=7.4\hat{i}-3.5\hat{j}$ and $\vec{B}=-8.5\hat{i}+4.6\hat{j}+2.0\hat{k}$. [Hint: To resolve an ambiguity, the dot product may prove useful.]

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

For the two vectors in Fig. E1.35, find the magnitude and direction of the vector product A x B

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