Given,
→A=3^i−2^j and →B=−^i−4^j
(a) →A+→B=(3^i−2^j)+(−^i−4^j)=2i−6j
(b) →A−→B=(3^i−2^j)−(−^i−4^j)=4i+2j
(c) ∣∣→A+→B∣∣=√22+(−6)2=√40
(d) ∣∣→A−→B∣∣=√42+22=√20
Direction of (→A+→B) is = →A+→B∣∣→A+→B∣∣=2^i−6^j√40
Direction of (→A−→B) is = →A−→B∣∣→A−→B∣∣=4^i+2^j√20