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RoseWind [281]
3 years ago
6

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

Mathematics
1 answer:
grandymaker [24]3 years ago
6 0
\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
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An electrician has a piece of wire that is 4 and 3/8 centimeters long. She divides the wire into pieces that are 1 and 2/3 centi
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3 years ago
If a varies directly as b, and a = 28 when b = 7, find b when a = 5.
Jlenok [28]

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Value of b = \frac{5}{4} =1.25.

Step-by-step explanation:

Direct Variation states that a relationship  between two variables in which one is a constant multiple of the other.

*if one variable changes the other changes in proportion to the first.

*If a is directly proportional to b i.e,  

a \propto b then it is of the form

a = kb     ;where k is constant variation.  

Given: a varies directly as b;

then, by definition of direct variation;

we have;

a = kb             .....[1]

Substitute the value of a =28 and b =7 to solve for k;

28 = k(7)

Divide both sides by 7 we have;

\frac{28}{7}=\frac{7k}{7}

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k =4

now, find b using same method when a =5;

then;

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5=(4)b

Divide by 4 to both sides we get;

b =\frac{5}{4}

Therefore, the value of b = \frac{5}{4} =1.25



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2 years ago
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