find the distance between
(-3,-2) & (-6,7),the axes being inclined at 60 degrees.

Asked by araima2001 | 25th Jun, 2016, 09:10: AM

Expert Answer:

begin mathsize 12px style For space oblique space coordinate space system comma
space where space the space axes space are space inclined space at space some space angle space straight theta comma
the space distance space between space two space points space open parentheses straight x subscript 1 comma space straight y subscript 1 close parentheses space and space open parentheses straight x subscript 2 comma space straight y subscript 2 close parentheses space is space given space by space
square root of open parentheses straight x subscript 1 minus straight x subscript 2 close parentheses squared plus open parentheses straight y subscript 1 minus straight y subscript 2 close parentheses squared plus 2 open parentheses straight x subscript 1 minus straight x subscript 2 close parentheses open parentheses straight y subscript 1 minus straight y subscript 2 close parentheses cosθ end root
In space the space given space problem comma space the space coordinates space of space two space points space are
open parentheses negative 3 comma space minus 2 close parentheses space and space open parentheses negative 6 comma space 7 close parentheses. space
The space angle space between space the space axes space is space 60 degree
Using space the space formula comma space we space get space the space distance space as
square root of open parentheses negative 3 minus open parentheses negative 6 close parentheses close parentheses squared plus open parentheses negative 2 minus 7 close parentheses squared plus 2 open parentheses negative 3 minus open parentheses negative 6 close parentheses close parentheses open parentheses negative 2 minus 7 close parentheses cos 60 degree end root
equals square root of 3 squared plus 9 squared plus 2 cross times 3 cross times negative 9 cross times 1 half end root
equals square root of 9 plus 81 minus 27 end root
equals square root of 63
end style

Answered by satyajit samal | 27th Jun, 2016, 09:23: AM