If |𝐴⃗ + 𝐵⃗| = 𝐴 + 𝐵 and neither 𝐴⃗ nor 𝐵⃗⃗ vanish, then:
A) 𝐴⃗ and 𝐵⃗ are parallel and in the same direction
B) 𝐴⃗ and 𝐵⃗ are parallel and in opposite directions
C) the angle between 𝐴⃗ and 𝐵⃗ is 45 degrees
D) the angle between 𝐴⃗ and 𝐵⃗ is 60 degrees
E) 𝐴⃗ is perpendicular to 𝐵⃗
Guide On Rating System
Vote
A) 𝐴⃗ and 𝐵⃗ are parallel and in the same direction
Explanation: If |𝐴⃗ + 𝐵⃗| = 𝐴 + 𝐵, then the vectors 𝐴⃗ and 𝐵⃗ must be pointing in the same direction in order for their magnitudes to add up to the sum of their magnitudes. If they were in opposite directions, their magnitudes would subtract from each other, not add. Additionally, if they were at an angle of 45 degrees or 60 degrees, their combined magnitude would be greater than 𝐴 + 𝐵. Therefore, the correct answer is that 𝐴⃗ and 𝐵⃗ are parallel and in the same direction.
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99