Vector X is collinear to vector a = (1; 2; -2). Forms an acute angle with the Oz axis.

univerkov | August 11, 2021 | education

Vector X is collinear to vector a = (1; 2; -2). Forms an acute angle with the Oz axis. Find the sum of the coordinates of the vector X, if | x | = 47.

Find the modulus of the vector:

| a | = √ (1 + 2 ^ 2 + (-2) ^ 2) = √ (1 + 4 + 4) = 3.

Then the collinearity coefficient is:

k = | x | / | a | = 47/3.

Vector X = (47/3; 2 * 47/3; -2 * 47/3) the sum of its coordinates will be:

47/3 + 2 * 47/3 – 2 * 47/3 = 47/3.

Answer: 47/3.

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