Question

If A=6i-8j,B=-8i-3j and C=26i+19j. Find a and b such that of aA+bB+C=0

Answer 1

Thank you

Answer 2

125

Answer 3

Yes

Answer 4

Myself

Answer 5

Answers

Answer 6

-2a-11b+45=0

Answer 7

Abdulaziz

Answer 8

Myself

Answer 9

[AI-generated answer — Explain Bot]

To find the values of a and b such that aA + bB + C = 0, we can equate the real and imaginary parts of the left-hand side to zero.

Let's start with the real parts:

Real part: a(Aₓ) + b(Bₓ) + Cₓ = 0
where Aₓ represents the x-coordinate of vector A, Bₓ represents the x-coordinate of vector B, and Cₓ represents the x-coordinate of vector C.

Plugging in the given values of A, B, and C:
a(6) + b(-8) + 26 = 0

Now, let's move on to the imaginary parts:

Imaginary part: a(Aᵧ) + b(Bᵧ) + Cᵧ = 0
where Aᵧ represents the y-coordinate of vector A, Bᵧ represents the y-coordinate of vector B, and Cᵧ represents the y-coordinate of vector C.

Using the given values of A, B, and C:
a(-8) + b(-3) + 19 = 0

Now we have a system of two equations:

6a - 8b + 26 = 0
-8a - 3b + 19 = 0

We can solve this system of equations using various methods, such as substitution or elimination. Let's use the elimination method:

Multiply the first equation by 8 and the second equation by 6 to eliminate the a term:

48a - 64b + 208 = 0
-48a - 18b + 114 = 0

Add the two equations together:

-82b + 322 = 0

Now, solve for b:

-82b = -322
b = -322 / -82
b = 3.93 (rounded to two decimal places)

Substitute the value of b into one of the earlier equations, let's use the first equation:

6a - 8(3.93) + 26 = 0
6a - 31.44 + 26 = 0
6a - 5.44 = 0
6a = 5.44
a = 5.44 / 6
a = 0.91 (rounded to two decimal places)

Therefore, the values of a and b that satisfy aA + bB + C = 0 are:
a = 0.91
b = 3.93

Answer 10

just add up the parts. You need

6a-8b+26 = 0
-8a-3b+19 = 0
Now just solve for a and b.