Question

Taking A= (6.00i–8.00j) units,B= (-8.00i+3.00j) units, and C= (26.0i+ 19.0j)units, determine a and b such that aA + Bb + C = 0.

Answer 1

Explanation:

aA=(6. 00ai-8.00aj)

bB=(-8.00bi+3.00bj)

aA+bB=[(6.00a-8.00b)i+(3.00b-8.00a)j]

aA+bB+C=[(6a-8b+26)i+(3b-8a+19)j]

aA+bB+C=0

So 6a-8b=(-26)

3a-4b=(-13) multiply it by 8 we get

24a-32b=(-104) - (equation 1)

Equating coefficient of j=0 we get

3b-8a=(-19) multiplying it by 3 we get

9b-24a=(-57) -(equation 2)

Adding equation 1 and 2 we g we get

-23b=(-161)

So b=7

Putting value of b in any one of the equation we get a=5

Answer 2

Answer:

A = 5 and B = 7

Explanation:

aA=(6. 00ai-8.00aj)

bB=(-8.00bi+3.00bj)

aA+bB=[(6.00a-8.00b)i+(3.00b-8.00a)j]

aA+bB+C=[(6a-8b+26)i+(3b-8a+19)j]

aA+bB+C=0

So 6a-8b=(-26)

3a-4b=(-13) multiply it by 8 we get

24a-32b=(-104) - (equation 1)

Equating coefficient of j=0 we get

3b-8a=(-19) multiplying it by 3 we get

9b-24a=(-57) -(equation 2)

Adding equation 1 and 2 we g we get

-23b=(-161)

So b=7

Putting value of b in any one of the equation we get a=5