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Question
Find the sum of the vectors a=^i−2^j+^k,
b=−2^i+4^j+5^k and c=^i−6^j−7^k.
Find the sum of the vectors a=^i−2^j+^k,
b=−2^i+4^j+5^k and c=^i−6^j−7^k.
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Solution
Here, given a=^i−2^j+^k,b=−2^i+4^j+5^k,c=^i−6^j−7^k
Sum of these vectors can be calculated by adding their ^i,^j and ^k components.
∴ a+b+c=(^i−2^j+^k)+(−2^i+4^j+5^k)+(^i−6^j−7^k) =(^i−2^i+^i)+(−2^i+4^j−6^j)+(^k+5^k−7^k) =0^i−4^j−^k=−4^j−^k
Here, given a=^i−2^j+^k,b=−2^i+4^j+5^k,c=^i−6^j−7^k
Sum of these vectors can be calculated by adding their ^i,^j and ^k components.
∴ a+b+c=(^i−2^j+^k)+(−2^i+4^j+5^k)+(^i−6^j−7^k) =(^i−2^i+^i)+(−2^i+4^j−6^j)+(^k+5^k−7^k) =0^i−4^j−^k=−4^j−^k
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