Let A and B be two vectors of magnitude 10 unit each. If they are inclined to the X-axis at angles 30 degree and 60 degree respectively, find the resultsnt

Asked by Anil | 8th Jun, 2017, 10:20: AM

Expert Answer:

begin mathsize 12px style Angle space between space the space vectors space straight theta equals space 60 degree minus 30 degree space equals 30 degree. space
Given space that space open vertical bar straight A with rightwards harpoon with barb upwards on top close vertical bar space and space open vertical bar straight B with rightwards harpoon with barb upwards on top close vertical bar space equals space 10 space unit
Hence space magnitude space of space the space resultant space is space
straight R space equals space square root of left parenthesis straight A ² plus straight B ² plus 2 ABcosθ end root right parenthesis space
space space space equals space square root of left parenthesis 10 ² plus 10 ² plus 2 space cross times space 10 space cross times space 10. cos 30 degree right parenthesis end root space
space space space equals square root of left parenthesis 200 plus 200 cross times √ 3 divided by 2 right parenthesis end root space
therefore space straight R space equals space 19.32 space units
Since space the space vectors space have space equal space magnitudes space so space the space resultant space bisects space the space angle space straight theta space between space them. space
Angle space between space resultant space and space vector space straight A space equals fraction numerator 30 degree over denominator 2 end fraction space equals 15 degree. space
So space angle space between space resultant space and space straight X minus axis space equals 15 degree plus 30 degree space equals 45 degree end style

Answered by Yashvanti Jain | 8th Jun, 2017, 11:26: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.