Question

The resultant of two vectors A and B is perpendicular to vector A and has the magnitude 24 cm.If the sum of magnitudes of vector A and vector B is 32 cm,then their magnitudes are
1) 5 cm, 27 cm
2) 7 cm ,25 cm
3) 14 cm,18 cm
4) 10 cm,22 cm

Answer 1

The resultant of two vectors A and B is perpendicular to vector A and has the magnitude 24 cm. If the sum of magnitudes of vector A and vector B is 32 cm, then their magnitudes are

1) 5 cm, 27 cm

2) 7 cm, 25 cm

3) 14 cm, 18 cm

4) 10 cm, 22 cm

From picture obviously:

$$a ^ {2} + s ^ {2} = b ^ {2}$$

the sum of magnitudes of vector A and vector B is 32 cm, therefore:

$$a = 3 2 - b$$

Substituting to first equation:

$$b ^ {2} - (3 2 - b) ^ {2} - 2 4 ^ {2} = 0$$ $$2 * 3 2 b = 3 2 ^ {2} + 2 4 ^ {2}$$

Then, b and a equals:

$$b = \frac {3 2 ^ {2} + 2 4 ^ {2}}{2 * 3 2} = 2 5$$ $$a = 3 2 - 2 5 = 7$$

Answer: 2) 7 cm, 25 cm