SOLUTION: Determine the value(s) of x such that the area of the parallelogram formed by the vectors a = (x + 1, 1, −2) and b = (x, 3, 0) is 41. There are little arrows above vectors a

Algebra ->  Test -> SOLUTION: Determine the value(s) of x such that the area of the parallelogram formed by the vectors a = (x + 1, 1, −2) and b = (x, 3, 0) is 41. There are little arrows above vectors a       Log On


   

Question 1163663: Determine the value(s) of x such that the area of the parallelogram formed
by the vectors a = (x + 1, 1, −2) and b = (x, 3, 0) is 41.
There are little arrows above vectors a and b. I just dont know how to type them in. Thank you.
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Area%22%22=%22%22abs%28abs%28matrix%281%2C3%2Ca%2Cx%2Cb%29%29%29

matrix%281%2C3%2Ca%2Cx%2Cb%29%22%22=%22%22abs%28matrix%283%2C3%2Ci%2Cj%2Ck%2Cx%2B1%2C1%2C-2%2Cx%2C3%2C0%29%29%22%22=%22%22%22%22=%22%22


%22%22=%22%22


%280%2B6%5E%22%22%29i-%280%2B2x%5E%22%22%29j%2B%283x%2B3-x%5E%22%22%29k%22%22=%22%226i-2xj%2B%282x%2B3%29k


Area%22%22=%22%22abs%28abs%28matrix%281%2C3%2Ca%2Cx%2Cb%29%29%29%22%22=%22%22abs%28abs%286i-2xj%2B%282x%2B3%29k%29%29%22%22=%22%22sqrt%286%5E2%2B%28-2x%29%5E2%2B%282x%2B3%29%5E2%29%22%22=%22%22


sqrt%2836%2B4x%5E2%2B4x%5E2%2B12x%2B9%29%22%22=%22%22sqrt%288x%5E2%2B12x%2B45%29%22%22=%22%2241

                               sqrt%288x%5E2%2B12x%2B45%29%22%22=%22%2241
                                   8x%5E2%2B12x%2B45%22%22=%22%2241%5E2
                                   8x%5E2%2B12x%2B45%22%22=%22%221681
                                   8x%5E2%2B12x-1636%22%22=%22%220
                                   2x%5E2%2B3x-409%22%22=%22%220
                                   x+=+%28-%283%29+%2B-+sqrt%28+%283%29%5E2-4%282%29%28-409%29%29%29%2F%282%282%29%29+
                                   x+=+%28-3+%2B-+sqrt%283281%29%29%2F%284%29+

The positive solution is x = 13.57000349, approximately.

Edwin

Answer by ikleyn(52812) About Me  (Show Source):
You can put this solution on YOUR website!
.

Edwin, really nice solution (!)


My congrats (!) (!)


But notice, please, that negative value of x is the solution, too (!)