1
Question
If a×b=2i+2j−k, a+b=i−3j−4k then
If a×b=2i+2j−k, a+b=i−3j−4k then
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Solution
The correct options are
A a=14i+14j+k;b=34i−134j−5k
B a=j+2k;b=i−4j−6k
D a=−14i+74j+2k;b=54i−194j−7k
Checking option (A)→a=14^i+14^j+^k→b=34^i−134^j−5^k→a+→b=14^i+14^j+^k+34^i−134^j−5^k^i−3^j−4^k=^i−3^j−4^kvalid option
Now for option (B)→a=^j+2^k→b=^i−4^j−6^k→a+→b=^j+2^k+^i−4^j−6^k^i−3^j−4^k=^i−3^j−4^kvalid option
Now for option (c) is wrong correct →b=54^i−194^j−6^k→a=−14^i+74^j+2^k→b=54^i−194^j−6^k→a+→b=−14^i+74^j+2^k+54^i−194^j−6^k^i−3^j−4^k=^i−3^j−4^kvalid option
Now for option (D) →a=12^i+12^j→b=34^i−134^j−4^k→a+→b=12^i+12^j+34^i−134^j−4^k54^i−114^j−4^k≠^i−3^j−4^k not valid option
A a=14i+14j+k;b=34i−134j−5k
B a=j+2k;b=i−4j−6k
D a=−14i+74j+2k;b=54i−194j−7k
Checking option (A)
→a=14^i+14^j+^k
→b=34^i−134^j−5^k
→a+→b=14^i+14^j+^k+34^i−134^j−5^k
^i−3^j−4^k=^i−3^j−4^k
valid option
Now for option (B)
→a=^j+2^k
→b=^i−4^j−6^k
→a+→b=^j+2^k+^i−4^j−6^k
^i−3^j−4^k=^i−3^j−4^k
valid option
Now for option (c) is wrong correct →b=54^i−194^j−6^k
→a=−14^i+74^j+2^k
→b=54^i−194^j−6^k
→a+→b=−14^i+74^j+2^k+54^i−194^j−6^k
^i−3^j−4^k=^i−3^j−4^k
valid option
Now for option (D)
→a=12^i+12^j
→b=34^i−134^j−4^k
→a+→b=12^i+12^j+34^i−134^j−4^k
54^i−114^j−4^k≠^i−3^j−4^k
not valid option
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