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CBSE Class 12-science Answered

 

find area of IIgm whose diagonals are represented by vectors

 d1 = 2i – j + k  d2 = 3i + 4j – k

i j and k and k are unit vector

Asked by haroonrashidgkp | 01 Nov, 2018, 07:32: PM
Expert Answer
begin mathsize 16px style top enclose straight d subscript 1 end enclose equals 2 straight i with hat on top minus straight j with hat on top plus straight k with hat on top comma space top enclose straight d subscript 2 end enclose equals 3 straight i with hat on top plus 4 straight j with hat on top minus straight k with hat on top
top enclose straight d subscript 1 end enclose cross times top enclose straight d subscript 2 end enclose equals open vertical bar table row cell straight i with hat on top end cell cell straight j with hat on top end cell cell straight k with hat on top end cell row 2 cell negative 1 end cell 1 row 3 4 cell negative 1 end cell end table close vertical bar equals open parentheses 1 minus 4 close parentheses straight i with hat on top minus open parentheses negative 2 minus 3 close parentheses straight j with hat on top plus open parentheses 8 plus 3 close parentheses straight k with hat on top equals negative 3 straight i with hat on top plus 5 straight j with hat on top plus 11 straight k with hat on top
open vertical bar top enclose straight d subscript 1 end enclose cross times top enclose straight d subscript 2 end enclose close vertical bar equals space square root of left parenthesis negative 3 right parenthesis squared plus 5 squared plus 11 squared end root equals square root of 9 plus 25 plus 121 end root equals square root of 155 space units
Area space of space parallelogram equals 1 half open vertical bar top enclose straight d subscript 1 end enclose cross times top enclose straight d subscript 2 end enclose close vertical bar equals 1 half cross times square root of 155 space units end style
Answered by Sneha shidid | 02 Nov, 2018, 09:38: AM
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