Mathematics, 04.09.2020 20:01, tyler9585

How to express a vector as a product of its length and direction?

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answered: nickboy52210

So the way to express a vector( v = 2i - 2j - 2k ) as a product of its length and direction is

$v = |v| u = \sqrt{12} (\frac{2}{ \sqrt{12} } , -\frac{2}{ \sqrt{12} }, - \frac{2}{ \sqrt{12} })$

Step-by-step explanation:

Generally a vector is expressed as a product of its length and direction using the formula below

$v = |v|\cdot u$

Here v is the vector

|v| is its magnitude (length)

u is its unit vector (direction)

Now let take an example

Let

v = 2i - 2j - 2k

The magnitude is mathematically evaluated as

$|v| = \sqrt{ 2^2 + (-2)^2 + (-2)^2 }$

$|v| = \sqrt{12}$

The unit vector is mathematically represented as

$u = \frac{v}{|v|}$

$u = \frac{ }{\sqrt{12} }$

$u = \frac{2}{ \sqrt{12} } , -\frac{2}{ \sqrt{12} }, - \frac{2}{ \sqrt{12} }$

$v = |v| u = \sqrt{12} (\frac{2}{ \sqrt{12} } , -\frac{2}{ \sqrt{12} }, - \frac{2}{ \sqrt{12} })$

answered: Guest

starting with:

5 + x - 12 = 2x - 7

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)

5 - 12 = x - 7 (combine and cancel x's from both sides)

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)

0 = x (add numbers together on both sides)

so in order for the equation to be true, x must be 0.

trying x = -0.5

5 + x - 12 = 2x - 7 (original equation)

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)

5 + -0.5 - 12 = -1 - 7 (did multiplication)

-7.5 = -8 (did addition on both sides)

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.

trying x = 0

5 + x - 12 = 2x - 7 (original equation)

5 + 0 - 12 = 2(0) - 7 (plug in value of x)

5 + 0 - 12 = 0 - 7 (did multiplication)

-7 = -7 (did addition on both sides)

since -7 equals -7, that demonstrates that the value of 0 for x is correct.

trying x = 1

5 + x - 12 = 2x - 7 (original equation)

5 + 1 - 12 = 2(1) - 7 (plug in value of x)

5 + 1 - 12 = 2 - 7 (did multiplication)

-6 = -5 (did addition on both sides)

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

answered: Guest

The answer would he -4,-2 because the points are just on the opposite side. since the x axis is +4 it's going to he -4 and since the y axis is -2 it stays there because whaen rotated it stays in the third quadrant
Hello! could someone with this problem?