Help me with geometry?

Compute a · (b ✕ c), where a = i − 3j + k, b = 4i + j + k and c = 9i − j + 3k.

grandymaker [24]

$\mathbf a=\mathbf i-3\,\mathbf j+\mathbf k$
$\mathbf b=4\,\mathbf i+\mathbf j+\mathbf k$
$\mathbf c=9\,\mathbf i-\mathbf j+3\,\mathbf k$

$\mathbf b\times\mathbf c=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\4&1&1\\9&-1&3\end{vmatrix}=4\,\mathbf i-3\,\mathbf j-13\,\mathbf k$

$\mathbf a\cdot(\mathbf b\times\mathbf c)=(\mathbf i-3\,\mathbf j+\mathbf k)\cdot(2\,\mathbf i-3\,\mathbf j-13\,\mathbf k)=4+(-3)^2-13=0$

6 0

3 years ago

There are 20 diamonds and 15 squares what is the ratio of squares to diamonds (REDUCE)

Inessa05 [86]

Its 15 to 20 which goes to 3 to 4

6 0

3 years ago

Read 2 more answers

How much pure acid should be mixed with 6 gallons of a 20% acid solution in order to get a 90% acid solution?

beks73 [17]

So, how much acid is there in 6 gallons? well is 20% acid or (20/100), so the amount of acid in it just (20/100) * 6 or 1.2, the rest is say water.

now, if we want a 90% solution, and say we add "y" gallons, how much acid is in it? well (90/100) * y, or 0.9y.

now let's add "x" gallons of pure acid, now, pure acid is just pure acid, so is 100% acid, how much acid is there in it? (100/100) * x, or 1x or just x.

we know whatever "x" and "y" amounts are, they -> x + 6 = y

and we also know that x + 1.2 = 0.9y

$\bf \begin{array}{lccclll}
&\stackrel{gallons}{acid}&\stackrel{acid~\%}{quantity}&\stackrel{acid~gallons}{quantity}\\
&------&------&------\\
\textit{pure acid}&x&1.00&x\\
\textit{20\% sol'n}&6&0.20&1.2\\
------&------&------&------\\\
mixture&y&0.90&0.9y
\end{array}
\\\\\\
\begin{cases}
x+6=\boxed{y}\\
x+1.2=0.9y\\
----------\\
x+1.2=0.9\left( \boxed{x+6} \right)
\end{cases}
\\\\\\
x+1.2=0.9x+5.4\implies x-0.9x=5.4-1.2\implies 0.1x=4.2
\\\\\\
x=\cfrac{4.2}{0.1}\implies x=\stackrel{gallons}{42}$

3 0

3 years ago

HELP!!!!!!!!!!

Vadim26 [7]

Answer:

A)Points are A ,B,C,D,G,E

B) other names are AC, CA, ABC

C)the Rays are DE, DG

D) M refers to the plane in which these points and Rays,lines are mentioned

E) < GDE < EDG are other names for angle 1

Explanation:

A line is one which has arrow heads on both ends and extends infinitely .

A ray has arrow Head at one end.

An angle is formed by the joining of two rays or lines.

Points are specific locations on a line or ray .

A plane has two dimensions length and breadth which has a line etc drawn on it

7 0

3 years ago

A restless point moved from point 12 to the left at the speed of 5/6 units per minute. Where will it be in 10.2 minutes? PLLLS H

mrs_skeptik [129]

Answer:

3.5

Step-by-step explanation:

4 0

4 years ago