If A=6i-8j,B=-8i+3j and C=26i+19j. Then,find "a"and "b" such that aA+bB+C=0
aA=bB+C = (6a-8b+26)i + (-8a+3b+19)j = 0i+0j
so solve those two equations to find a,b
If A=6i-8j,B=8i+3jand C=26i+19j find a and b that aA+bB+C=0
Ididn'tknow the ansewr
To find the values of "a" and "b", we need to equate the sum of "aA" and "bB" with the vector "C" and solve for "a" and "b".
Let's set up the equation:
aA + bB + C = 0
Substituting the given values of vectors A, B, and C:
a(6i - 8j) + b(-8i + 3j) + (26i + 19j) = 0
Now, let's expand the equation:
(6ai - 8aj) + (-8bi + 3bj) + 26i + 19j = 0
Combine the like terms:
(6a - 8b + 26)i + (-8a + 3b + 19)j = 0
Since the coefficients of both "i" and "j" are equated to zero, we can set up two equations based on the coefficients:
6a - 8b + 26 = 0 -- (1)
-8a + 3b + 19 = 0 -- (2)
We now have a system of linear equations. To solve for "a" and "b", we can use any suitable method, such as substitution or elimination. Let's use the elimination method in this case:
To eliminate one variable, multiply equation (1) by 8 and equation (2) by 6:
48a - 64b + 208 = 0 -- (3)
-48a + 18b + 114 = 0 -- (4)
Now, add equation (3) and equation (4):
-46b + 322 = 0
Solve for "b":
-46b = -322
b = -322 / -46
b = 7
Substitute the value of "b" back into equation (1):
6a - 8(7) + 26 = 0
6a - 56 + 26 = 0
6a - 30 = 0
6a = 30
a = 30 / 6
a = 5
Therefore, the values of "a" and "b" such that aA + bB + C = 0 are a = 5 and b = 7.