Given a right-angled triangle ABC with hypotenuse AC = 13 cm and leg BC = 5 cm.

Given a right-angled triangle ABC with hypotenuse AC = 13 cm and leg BC = 5 cm. Segment SA = 12 cm, – perpendicular to plane ABC. find | AS + SC + CB | (vectors)

According to the rule of addition of vectors, the sum of vectors | AS + SC + CB | = | AB |.

To determine the length of the vector | AB |, consider a right-angled triangle ABC, in which the angle B is straight, hypotenuse AC = 13 cm, leg BC = 5 cm. By the Pythagorean theorem, we find the value of leg AB.

AB ^ 2 = AC ^ 2 – BC ^ 2 = 13 ^ 2 – 5 ^ 2 = 169 – 25 = 144 cm.

AB = 12 cm.

Then | AS + SC + CB | = | AB | = 12 cm.

Answer: Sum of vectors | AS + SC + CB | = 12 cm.

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