Question
Mon July 09, 2012 By: Nevin
 

sir/madam if a,b,c are 3 non zero vectors such that a X b = c and b X c = a prove that a,b,c are mutually at right angles and |b | = 1 and |c| = |a|

Expert Reply
Sun July 22, 2012
Answer : Given : if a,b,c are 3 non zero vectors such that a X b = c and b X c = a
To prove: a,b,c are mutually at right angles and |b | = 1 and |c| = |a|
 
As we know that , 
a X b = c and b X c = a => c is perpendicular to a and b,
                                        also a is perpendicular to b and c
=> a ,b , c are mutually at right angle.
 
|a X b| = |c| and | b X c | = |a| 
=>|a| |b| sin90= |c| and |b| |c| sin90 = |a|   {as a ,b , c are mutually at right angle}
=> |a| |b|= |c| and |b| |c|  = |a|        {as sin90=1}....(1)
=>  |a| |b|= |c| and |b| |c| {|b|}  = |a| |b|
=> |b|2 |c|  = |c|         => |b| = 1         
=> |a| = |c|                                           { from (1) }
Hence proved
Related Questions
Fri January 27, 2017

 

Mon January 23, 2017

     

Home Work Help