If a=i+3j+k and b=i+12j+k, find a unit vector with positive first coordinate orthogonal to both a and

1 answer:

5 0

The cross product of the vectors will be orthogonal to both:
axb
[tex]=<1,3,1>x<1,12,1>
=
i j k
1 3 1
1 12 1
=<3-12, -1+1, 12-3>
=<-9,0,9>
Since it is required to have positive first coordinate, we reverse the sign of the components, namely reverse the direction of the vector, which is still orthogonal to both a and b:
Required vector is <9,0,-9> which is orthogonal to both a and b.

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How do I solve for x

Alchen [17]

Greetings!

To find the length of any side of a right triangle, you can use the Pythagorean Thereom. It states that the squares of two sides are equal to the square of the hypotenuse:
$a^2+b^2=c^2$

Input the information from the diagram into the formula:
$(x)^2+(x+7)^2=(13)^2$

Expand each term:
$(x)^2+(x+7)^2=(13)^2$

$x^2+((x+7)(x+7))=169$

$x^2+(x(x+7)+7(x+7))=169$

$x^2+x^2+7x+7x+49=169$

Combine like terms:
$2x^2+14x+49=169$

Add -169 to both sides:
$(2x^2+14x+49)+(-169)=(169)+(-169)$

$2x^2+14x-120=0$

Factor out the Common Term (2):
$2(x^2+7x-60)=0$

Factor the Complex Trinomial:
$2(x^2-5x+12x-60)=0$

$2(x(x-5)+12(x-5))=0$

$2(x-5)(x+12)=0$

Set Factors to equal 0:
$x-5=0$

$x=5$

or

$x+12=0$

$x=-12$

However, since we are solving for the side length, the only possible answer is 5 (a shape can't have a side with a negative length.)

The Solution Is:
$\boxed{x=5}$

I hope this helped!
-Benjamin

6 0

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A bottle contains 4 cups of juice. One serving of the juice À cup. How many servings are in the bottle?

Brilliant_brown [7]

4 servings if one serving per cup

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3 years ago

Read 2 more answers

Seven less than three times a number is 5. Find the number

Anit [1.1K]

Step-by-step explanation:

it is 12 because 12 - 7 is 5 the number 4 is the number multiplied by 3