Let p be the plane in space that intersects the x-axis at −5, the y-axis at −2, and the z-axis at 5. find a vector v¯¯¯ that is perpendicular to p.

To find a vector perpendicular to a given plane, is necessary to find two vectors on the plane and get the vector product of these two vectors.

Solution is:

PQ * PR = - 10×i + 10×k + 25×j

We must go through the following procedure:

Identifying the three points on the plane.

The three intersects are three points on the plane, these are:

P ( -5 , 0 , 0 ).        Q ( 0 , - 2 , 0 ).     R ( 0 , 0 , 5 )

From these points we get the vectors PQ and PR

PQ = ( 0 , -2 , 0 ) - ( -5 , 0 , 0 )

PQ = ( 0 - ( -5) , -2 - 0  , 0 - 0 )

PQ = ( 5 , - 2 , 0 )

PR = ( 0 , 0, 5 ) - ( -5 , 0, 0 )

PR = ( 5 , 0, 5 )

Now we get the vector product ( it is a perpendicular vector to PQ and PR ), and  is perpendicular to the plane.

                     i        j        k

PQ * PR =    5     -2       0      = i × (-2)×(5) + 0×k + 0×j

                    5      0       5         - [( -2)×5×k + (0)×(0)×i + (5)×(5)×j

PQ * PR = - 10×i + 10×k + 25×j

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Let P be the plane that intersects

Write the equation of the plane P:

Then

The coefficients at variables x, y and z are the coordinates of perpendicular vector to the plane. Thus

the camry sales+accord sale=828,000. to make it so the two numbers are 18 thousand apart and still equal 828,000, you first need to find out what half of 828,000 is. 828,000/2=414,000. for the two numbers to equal 828,000, you have to add the same amount as you subtract from the middle. in this case, the number is 9,000 because it's half of 18,000. to equal 828,000, you have to add 9,000 to 414,000 for the camry and subtract 9,000 from 414,000 for the accord. 414,000+9,000=423,000.

414,000-9,000=405,000.

423,000+405,000=828,000.

423,000-405,000=18,

hope it