For the following problem, find the direction cosines and direction angles for the position vector to the given point.

(5,7,-1)

For the following problem, find a particular equation of the plane described.

Perpendicular to $\vec{n}=-\vec{i}+3 \vec{j}-2 \vec{k}$, containing the point (4,7,5)

For the following problem, draw the position vector on graph paper. Show the circumscribed "box" that makes the vector look three-dimensional. Write the coordinates of the point at the head of the vector.

$$\vec{p}=10 \vec{\imath}+7 \vec{j}+3 \vec{k}$$

For the following problem, find the cross product using determinants.

$$(-3 \vec{i}+8 \vec{j}+2 \vec{k}) \times(\vec{i}+7 \vec{j}+6 \vec{k})$$

Find the point on the line in the previous problem for which d = 27.

For $\vec{a}$ and $\vec{b}$ in the previous part, find the position vector to the point 70% of the way from the head of $\vec{a}$ to the head of $\vec{b}$.

If $\vec{a}$ and $\vec{b}$ in the previous part are position vectors, find the displacement vector from the head of $\vec{a}$ to the head of $\vec{b}$.

Find a unit vector in the direction of $\vec{a}$ in the previousp art.

Find $|\vec{a}|$ for $\vec{a}$ in the previous part.

Refer to vectors $\vec{a}$ and $\vec{b}$ in the figure mentioned.

Find $\vec{a}-\vec{b}$ numerically from the coordinates of $\vec{a}$ and $\vec{b}$, and show that the answer agrees with your drawings in parts $a$ and $b$.

If $\vec{a}=6 \vec{i}-5 \vec{j}+2 \vec{k}$ and $\vec{b}=3 \vec{i}+4 \vec{j}-7 \vec{k}$, find $3 \vec{a}-2 \vec{b}$.

Refer to vectors $\vec{a}$ and $\vec{b}$ in the figure mentioned.

Draw a displacement vector from the head of $\vec{b}$ to the head of $\vec{a}$. Explain why this vector is equivalent to $\vec{a}-\vec{b}$ from part a. Explain verbally how you can tell whether $\vec{a}-\vec{b}$ goes from $\vec{a}$ to $\vec{b}$ or from $\vec{b}$ to $\vec{a}$.

Draw $\vec{v}=5 \vec{i}+9 \vec{j}+4 \vec{k}$ as a position vector. Show the "box" that makes it look three dimensional. Indicate the unit vectors $\vec{i}, \vec{j}$, and $\vec{k}$ on the drawing.

Refer to vectors $\vec{a}$ and $\vec{b}$ in the figure mentioned.

On another copy of the figure, draw $-\vec{b}$, the opposite of vector $\vec{b}$, as a position vector (starting at the origin). Then translate $-\vec{b}$ so that its tail is at the head of $\vec{a}$. Using the definition of vector addition, draw vector $\vec{a}+(-\vec{b})$. Explain why $\vec{a}-\vec{b}$ is equivalent to $\vec{a}+(-\vec{b})$.