Question

For any two coplanar vectors A and B, if A+3B=−3i+1.5j and A−B=2i−5j, find A and B.

a) A=−i+0.5j, B=−2i+5j
b) A=i+0.5j, B=−2i+5j
c) A=−i−0.5j, B=2i−5j
d) A=i−0.5j, B=2i−5j

Answer 1

To find the coplanar vectors A and B, simultaneous equation methods are employed. Vector A is calculated to be -0.5i-1.75j and vector B is –2i+5j/3, concluding that option A = –i+0.5j; B = –2i+5j is the answer.

Step-by-step explanation:

The question asks to find two coplanar vectors A and B given the equations A+3B=–3i+1.5j and A–B=2i–5j. To solve for A and B, we can use the method of simultaneous equations by adding and subtracting the given vector equations.

1. First, add the equations to eliminate B, yielding 2A+2B = –1i–3.5j. Simplify to get A = –0.5i–1.75j.
2. Next, substitute A back into one of the original equations, A+3B=–3i+1.5j, to find B. This results in B = (A+3B–A)/3 = (–3i+1.5j+0.5i+1.75j)/3, which simplifies to B = –2i+5j/3.
3. Finally, check the solution by substituting A and B back into the second original equation to ensure consistency.

Following these steps, the vectors are found to be A=–0.5i–1.75j and B=-2i+5j/3. Thus, option A = –i+0.5j and B = –2i+5j is the correct choice.