Question

Give only method in detail, no solution required.

:)

Answer 1

Here we have been given the value of vector A, B and C

We have to find the value of a and b, from the given equation.

Equation: aA+bB+C=0

 here we have the previlage to change the 1st and 2nd term by changing value of a and b, but C cannot be changed.

Hence send C to RHS:

we get the equation as :

aA+bB=  -C

(6a i  + 8a j) + (-8b i +3b j) = -26i -19j

Get i unit vector and j unit vector together.
and equate i vector from LHS to i From RHS , same way j 

(6a - 8b)i =  -26 i

(-8a+3b)j = -19 j

Write it as equation without i, and j

6a-8b = -26 ................(1)

-8a+3b=-19.................(2)

Solve both the equation get the value of a and b.

Since you have not asked for the solution, i m not adding it here. :P

Hope it helps...!!!!

Answer 2

wow ; its a vector question
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see answer step by step I hope you will learn this concept .

given,
A = 6i - 8j
B = - 8i +3j
C = 26i +19 j

Question says that
aA + bB + C = 0

here first of all we know ,
if any vector ,
xi +yj + zk = 0
it means ,
xi + yj +zk = 0i + 0j + 0k

x = 0
y = 0
z = 0
applied this concept here

now,
aA +bB + C = 0
a( 6i -8j ) + b( -8i + 3j) + ( 26i + 19j) =0

( 6a -8b +26)i +( -8a +3b +19)j = 0i + 0j

6a -8b +26 = 0
-8a +3b +19 = 0 now solve this equations

-32b +9b +104 +57 = 0
-23b + 161 = 0
b = 7

so, a = 5

hence, a = 5 and b = 7