 Hello and welcome to the session. In this session we are going to discuss the following question which says that find the volume of the parallel of pipette whose coterminous edges are represented by the vectors pipe i cap plus 4 j cap plus 10 cap, 3 i cap plus 2 j cap plus 4 k cap and 2 i cap plus j cap minus k cap volume of the parallel of pipette with vector abc as coterminous edges is given by the scalar triple product of vector abc with this key idea let us proceed with the solution vector ab equal to 5 i cap plus 4 j cap plus 10 k cap, vector bb equal to 3 i cap plus 2 j cap plus 4 k cap and vector c b equal to 2 i cap plus j cap minus k cap and from the key idea we know that volume of the parallel of pipette with vector abc as coterminous edges is given by the scalar triple product of vector abc therefore volume of the parallel of pipette is given by the scalar triple product of vector abc which is given by the determinant of vector ab and c where the first row of the determinant is given by the coefficient of the unit vectors of the vector a that is 5, 4 and 10 second row is the coefficient of the unit vectors of the vector b that is 3, 2, 4 and third row is the coefficient of the unit vectors of vector c that is 2, 1 and minus 1 on solving further we get 5 into 2 into minus 1 that is minus 2 minus of 1 into 4 that is 4 minus 4 into 3 into minus 1 that is minus 3 minus 2 into 4 that is 8 plus 10 into 3 into 1 that is 3 minus of 2 into 2 that is 4 which is equal to 5 into minus 6 minus 4 into minus 11 plus 10 into minus 1 that is minus 30 plus 44 minus 10 which is equal to 4 hence the volume of the parallel of pipette is given by 4 cubic units this is the required answer this completes our session hope you enjoyed this session