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Home / Doubts and Solutions/JEE-BASIC/Class 6/Mathematics

Sir, how do I prove that 3 points A,B and C with position vectors :
-2 i+ 3 j +5 k  ,   i + 2 j + 3 k   and 7 i - k 
are collinear ?? please help me sir..i would be grateful... 

Asked by Aditya Bikram Chakraborty 7th September 2015, 6:05 PM
Answered by Expert
Answer:

C o n s i d e r space t h e space v e c t o r s A equals negative 2 i with overbrace on top plus 3 j with overbrace on top plus 5 k with overbrace on top B equals i with overbrace on top plus 2 j with overbrace on top plus 3 k with overbrace on top C equals 7 i with overbrace on top minus k with overbrace on top N o w space c o n s i d e r B minus A equals open parentheses i with overbrace on top plus 2 j with overbrace on top plus 3 k with overbrace on top close parentheses minus open parentheses negative 2 i with overbrace on top plus 3 j with overbrace on top plus 5 k with overbrace on top close parentheses space space space space space space space space space equals 3 i with overbrace on top minus j with overbrace on top minus 2 k with overbrace on top C minus A equals open parentheses 7 i with overbrace on top minus k with overbrace on top close parentheses minus open parentheses negative 2 i with overbrace on top plus 3 j with overbrace on top plus 5 k with overbrace on top close parentheses space space space space space space space space space equals 9 i with overbrace on top minus 3 j with overbrace on top minus 6 k with overbrace on top space space space space space space space space space space equals 3 open parentheses 3 i with overbrace on top minus j with overbrace on top minus 2 k with overbrace on top close parentheses space space space space space space space space space space equals 3 open parentheses B minus A close parentheses T h u s comma space C minus A space i s space p r o p o r t i o n a l space t o space B minus A H e n c e space A comma B space a n d space C space a r e space c o l l i n e a r.

Answered by Expert 7th September 2015, 6:30 PM
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