Question

If a vector a - b = 2c, a + b = 4c and c = 3i + 4j,find a and b

Answer 1

Ans:
a = 9i + 12j
b = 3i + 4j

Explanation:
We have two equations:

a - b = 2c --- (A)
a + b = 4c --- (B)

and two unknowns:
a = ?
b = ?

Whereas,
c = 3i + 4j

Add equations (A) and (B):
=> a - b = 2c
     a + b = 4c
----------------------
    2a = 6c

=> a = 3c --- (C)
Put the value of vector c in equation (C):

(C) => a = 3(3i + 4j)
=> a = 9i + 12j

Now that we have vector a, put that vector and vector c in equation (A):
(A)=> (9i + 12j) - b = 2(3i + 4j)

=> b = (9i + 12) - (6i + 8j)
=> b = 3i + 4j

Ans:
a = 9i + 12j
b = 3i + 4j