The coordinates of the point C (3; -2; 0) and B (5; 2; 3) are known. Find the coordinates and length of the vector CB.

| September 16, 2021 | education

To find the coordinates of the vector CB, knowing the coordinates of its start point C and end point B, it is necessary to subtract the corresponding coordinates of the start point from the coordinates of the end point. That is, if the vector CB is given by the coordinates of the points C (Cx; Cy; Cz) and B (Bx; By; Bz) can be found using the following formula: CB = (Bx – Cx; By – Cy; Bz – Cz).

The length of the directed segment determines the numerical value of the vector and is called the vector length or the modulus of the CB vector. The modulus of the vector CB = (CBx; CBy; CBz) can be found using the formula: | CB | = √ (CBx2 ^ + CBy ^ 2 + CBz ^ 2).

Find the vector CB by the coordinates of the points: CB = (Bx – Cx; By – Cy; Bz – Cz) = (5 – 3; 2 – (-2); 3 – 0) = (2; 4; 3).

Find the length (modulus) of the vector CB: | CB | = √ (CBx ^ 2 + CBy ^ 2 + CBz ^ 2) = √ (2 ^ 2 + 4 ^ 2 + 3 ^ 2) = √ (4 + 16 + 9) = √29.

Answer: the coordinates of the vector are the length of the vector CB (2; 4; 3), the length is √29.



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