Let A= 3i + 4j - 2k nad B= 2i + 2j +2k. Find C such that - 7B + C = 0. I NEED TO

Question

Let A= 3i + 4j - 2k nad B= 2i + 2j +2k. Find C such that - 7B + C = 0.

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Explanation / Answer

We want to find the value of c such that: x^2 - 6x + c = 0, has one one solution. To do this, we can use the discriminant. Recall that a quadratic equation has one real solution when the discriminant equals zero. Since the discriminant of ax^2 + bx + c = 0 is b^2 - 4ac, the discriminant of x^2 - 6x + c = 0 is: (-6)^2 - 4(1)(c) = 36 - 4c. Therefore, one real solution exists when: 36 - 4c = 0 ==> c = 9. Line y = 3/2 x + 6 has slope = 3/2 Let f(x) = cvx Then f'(x) = c/(2vx) Now we need to find values of x and c so that slope of curve at x = slope of line f'(x) = 3/2 c/(2vx) = 3/2 c = 3vx Substituting this back into equation of curve, we get f(x) = cvx = (3vx)vx = 3x Now we find x where f(x) intersects line 3/2 x + 6 3x = 3/2 x + 6 6x = 3x + 12 3x = 12 x = 4 c = 3vx = 3v4 = ±6 When c = -6, f(x) = -6vx and f'(x) = -3/vx < 0. But slope of line = 3/2 > 0 Therefore c = -6 is not valid ANSWER: c = 6

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