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o-na [289]
3 years ago
6

Building a is 271 meters taller than building

Mathematics
1 answer:
kvv77 [185]3 years ago
4 0

Let a and b represent the heights of the corresponding buildings (in meters).

... a = b +271 . . . . . . . a is 271 meters taller than b

... 2b -a = 211 . . . . . . if a is subtracted from twice b, the result is 211

Use the expression for a in the first equation to substitute for a in the second.

... 2b - (b+271) = 211

... b = 482 . . . . . . . . . . . simplify and add 271

... a = b +271 = 753

Building a is 753 meters tall; building b is 482 meters tall.

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1/2d + 6 = 1/2 (d + 3)

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Find two unit vectos that are orthogonal to both [0,1,2] and [1,-2,3]
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Answer:

Let the vectors be

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b = [1, -2, 3]

( 1 ) The cross product of a and b (a x b) is the vector that is perpendicular (orthogonal) to a and b.

Let the cross product be another vector c.

To find the cross product (c) of a and b, we have

\left[\begin{array}{ccc}i&j&k\\0&1&2\\1&-2&3\end{array}\right]

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( 2 ) Convert the orthogonal vector (c) to a unit vector using the formula:

c / | c |

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Therefore, the unit vector is

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The other unit vector which is also orthogonal to a and b is calculated by multiplying the first unit vector by -1. The result is as follows:

[ \frac{-7}{3\sqrt{6} } , \frac{-2}{3\sqrt{6} } , \frac{1}{3\sqrt{6} } ]

In conclusion, the two unit vectors are;

[ \frac{7}{3\sqrt{6} } , \frac{2}{3\sqrt{6} } , \frac{-1}{3\sqrt{6} } ]

and

[ \frac{-7}{3\sqrt{6} } , \frac{-2}{3\sqrt{6} } , \frac{1}{3\sqrt{6} } ]

<em>Hope this helps!</em>

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