Find the maximum rate of change off at the given point and the direction in which it occurs.f(x, y) = 4y sqrt(x), (4,1)

Find a vector equation and parametric equations for the line segment that joins P to Q.
P(0, - 1, 1), Q(1/2, 1/3, 1/4)

Find the scalar and vector projections of b onto a.
$a=(4,7,-4),b=(3,-1,1)$

Which of the following expressions are meaningful? Which are meaningless? Explain.
a) $(a\cdot b)\cdot c$
$(a\cdot b)\cdot c$ has ? because it is the dot product of ?.
b) $(a\cdot b)c$
$(a\cdot b)c$ has ? because it is a scalar multiple of ?.
c) $|a|(b\cdot c)$
$|a|(b\cdot c)$ has ? because it is the product of ?.
d) $a\cdot (b+c)$
$a\cdot (b+c)$ has ? because it is the dot product of ?.
e) $a\cdot b+c$
$a\cdot b+c$ has ? because it is the sum of ?.
f) $|a|\cdot (b+c)$
$|a|\cdot (b+c)$ has ? because it is the dot product of ?.

Let F be a fixed 3x2 matrix, and let H be the set of all matrices A in ${\displaystyle M_{2\times 4}}$ with the property that FA = 0 (the zero matrix in ${\displaystyle M_{3\times 4})}$. Determine if H is a subspace of ${\displaystyle M_{2\times 4}}$

Find the scalar and vector projections of b onto a.
${\displaystyle a=(4,7,-4),b=(3,-1,1)}$

(-2,3)+(-1,6)=?

Find an equation for the plane containing the two (parallel) lines
${\displaystyle v_1=(0,1,-2)+t(2,3,-1)}$
${\displaystyle v_2=(2,-1,0)+t(2,3,-1)}$