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Consider three vectors vector A, vector B, vector C. It is given that vector A and vector B lie in the x-y plane and the direction of vector C is along (+k^). Also, it is known that |vector A|=10 and |vector B|=6 units and the three vectors are related by the relation vector A=vector B - alpha(vector B X vector C), where alpha is some postive constant. Now, if only the magnitude of vector C is doubled, then what should the magnitude of vector B be, for which vector A remains unchanged (both in magnitude and direction)?

Asked by sd8022567 9th June 2022, 1:02 PM
Answered by Expert
Answer:
It is given that begin mathsize 14px style A with rightwards arrow on top end style and begin mathsize 14px style B with rightwards arrow on top end style are in x-y plane and begin mathsize 14px style C with rightwards arrow on top end style is along z-axis .
begin mathsize 14px style A with rightwards arrow on top end style , begin mathsize 14px style B with rightwards arrow on top end style and begin mathsize 14px style C with rightwards arrow on top end style are related as
begin mathsize 14px style A with rightwards arrow on top end style = begin mathsize 14px style B with rightwards arrow on top end style - α ( begin mathsize 14px style B with rightwards arrow on top end style × begin mathsize 14px style C with rightwards arrow on top end style )   ...................... (1)
let begin mathsize 14px style D with rightwards arrow on top end style = α ( begin mathsize 14px style B with rightwards arrow on top end style × begin mathsize 14px style C with rightwards arrow on top end style )  .........................(2)
Hence we get , begin mathsize 14px style A with rightwards arrow on top end style + begin mathsize 14px style D with rightwards arrow on top end style = begin mathsize 14px style B with rightwards arrow on top end style .......................(3)
From the given orientaion of vectors , we can see that begin mathsize 14px style D with rightwards arrow on top end style is in x-y plane .
Hence  begin mathsize 14px style A with rightwards arrow on top end style , begin mathsize 14px style B with rightwards arrow on top end style and begin mathsize 14px style D with rightwards arrow on top end style are coplanar . begin mathsize 14px style B with rightwards arrow on top end style is resultant of begin mathsize 14px style A with rightwards arrow on top end style and begin mathsize 14px style D with rightwards arrow on top end style.
Answered by Expert 10th June 2022, 10:46 AM
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