If c vector = 3 a vector + 4 b vector and 2 c vector = a vector – 3 b vector ,

show that

(i) c vector and a vector have the same direction and | c vector | > |a| vector

(ii) c vector and b vector have opposite direction and | c vector | >|b vector|

C= 3A+ 4B.............. i
and
2C=A-3B..................ii
=> multiply i by 3 and ii to 4 and add
3C+8C=9A+12B+4A-12B
11C=13A=> |C|/|A| =13/11
so C and A are in same direction and magnitude of C is more than that of A

similarly multiply i by 1 and ii by 3 and substract
C-6C=4B+9B=> -5C=11B
|C|/|B|=11/5
So C, B are opposite direction with magnitude of C is more than B