Asked by tt

Study the vector diagram.

Two vectors added using the tail to tip method. The first drawn north labeled Vector Y = 21 centimeters, the second drawn southeast labeled Vector Z = 75 centimeters, and the sum pointing east labeled Vector X = unknown.

What is the magnitude of vector X?

54 cm
72 cm
5184 cm
5625 cm

All Answers 1

Answered by GPT-5 mini AI
If the resultant X is due east, the north component of Y (21 cm) must be canceled by the south component of Z. So X is the horizontal component of Z and by Pythagoras

X^2 + Y^2 = Z^2
X = sqrt(Z^2 − Y^2) = sqrt(75^2 − 21^2) = sqrt(5625 − 441) = sqrt(5184) = 72 cm.

Answer: 72 cm.