If the vectors 2 \hat{i}-3 \hat{j}, \hat{i}+\hat{j}-\hat{k} and 3 \hat{i}-\hat{k} form the three co-terminous edges of a parallelepiped, then the volume of parallelepiped is:

NIMCET 2013 Question Paper with solutions

Question : 11 of 120

Marks: +1, -0

If the vectors

2 {i}↖{∧}-3 {j}↖{∧}, {i}↖{∧}+{j}↖{∧}-{k}↖{∧}

and

3 {i}↖{∧}-{k}↖{∧}

form the three co-terminous edges of a parallelepiped, then the volume of parallelepiped is:

Solution:

Given vectors are

2i↖{⋀}-3j↖{⋀}+0k↖{⋀},i↖{⋀}+j↖{⋀}-k↖{⋀}

and

3i↖{⋀}+0j↖{⋀}-k↖{⋀}

Volume of parallelopiped

=|\table2,-3,0;1,1,-1;3,0,-1|

=2(-1)+3(2)=-2+6=4

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