three vectors a,b and c are given as?

Question

a=xi-11j+13k
b=-11i+xj-7k
c=13i-7j+xk
Find the largest value of x for which the magnitude of the resultant of the three vectors is equal to 19.

Answer 1

Resultant = (2+x)i + (x-18)j + (6+x)k
Magnitude = 19
sqrt[(2+x)^2 + (x-18)^2 + (6+x)^2] = 19
4+4x+x^2 + x^2-36x+324 + 36+12x+x^2 = 361
3x^2 - 20x + 3 = 0
x = [20 +- sqrt(20^2 - 4(3)(3)] / (2)(3)
x = [20 +- 19.08] / 6
x = 6.51, 0.153

So the largest value of x is 6.51.

Answer 2

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