Question

(i) State the two main properties of a vector. 2% of paper. Let $\vec{a} = 3\hat{i} - \hat{j} - 2\hat{k}$, $\vec{b} = -4\hat{i} - 4\hat{j} - \hat{k}$, $\vec{c} = \hat{i} - \hat{j}$. (ii) Find $||\vec{a} \times \vec{c}||$. (iii) Compute $3\vec{a} - 7\vec{b}$. 3% of paper. 2% of paper. (iv) Are $\vec{b}$ and $\vec{c}$ perpendicular? Explain your answer. 3% of paper. (v) Find the vector projection of $\vec{b}$ on to $\vec{a}$. 4% of paper. (vi) Find the area of a parallelogram spanned by the vectors $\vec{a}$ and $\vec{c}$. 6% of paper. (vii) Find the volume of the parallelepiped spanned by the vectors $\vec{a}$, $\vec{b}$ and $\vec{c}$. 3% of paper. (viii) Are $\vec{a}$, $\vec{b}$ and $\vec{c}$ coplanar? Explain your answer. 2% of paper.

          (i) State the two main properties of a vector. 2% of paper.
Let $\vec{a} = 3\hat{i} - \hat{j} - 2\hat{k}$,
$\vec{b} = -4\hat{i} - 4\hat{j} - \hat{k}$,
$\vec{c} = \hat{i} - \hat{j}$.
(ii) Find $||\vec{a} \times \vec{c}||$.
(iii) Compute $3\vec{a} - 7\vec{b}$.
3% of paper.
2% of paper.
(iv) Are $\vec{b}$ and $\vec{c}$ perpendicular? Explain your answer.
3% of paper.
(v) Find the vector projection of $\vec{b}$ on to $\vec{a}$.
4% of paper.
(vi) Find the area of a parallelogram spanned by the vectors $\vec{a}$ and $\vec{c}$.
6% of paper.
(vii) Find the volume of the parallelepiped spanned by the vectors $\vec{a}$, $\vec{b}$ and $\vec{c}$.
3% of paper.
(viii) Are $\vec{a}$, $\vec{b}$ and $\vec{c}$ coplanar? Explain your answer.
2% of paper.

(i) State the two main properties of a vector. 2% of paper.
Let a⃗ = 3î - ĵ - 2k̂,
b⃗ = -4î - 4ĵ - k̂,
c⃗ = î - ĵ.
(ii) Find ||a⃗×c⃗||.
(iii) Compute 3a⃗ - 7b⃗.
3% of paper.
2% of paper.
(iv) Are b⃗ and c⃗ perpendicular? Explain your answer.
3% of paper.
(v) Find the vector projection of b⃗ on to a⃗.
4% of paper.
(vi) Find the area of a parallelogram spanned by the vectors a⃗ and c⃗.
6% of paper.
(vii) Find the volume of the parallelepiped spanned by the vectors a⃗, b⃗ and c⃗.
3% of paper.
(viii) Are a⃗, b⃗ and c⃗ coplanar? Explain your answer.
2% of paper.

Added by Carmen P.

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