Advertisement Remove all ads

Find → a . ( → B × → C ) , If → a = 2 ^ I + ^ J + 3 ^ K , → B = − ^ I + 2 ^ J + ^ K and → C = 3 ^ I + ^ J + 2 ^ K . - Mathematics

Short Note
Sum

Find \[\vec{a} . \left( \vec{b} \times \vec{c} \right)\],  if \[\vec{a} = 2 \hat {i} + \hat {j} + 3 \hat {k} , \vec{b} = - \hat {i} + 2 \hat {j} + \hat {k}\] and  \[\vec{c} = 3 \hat { i} + \hat {j} + 2 \hat {k}\].

Advertisement Remove all ads

Solution

The given vectors are \[\vec{a} = 2 \hat {i} + \hat {j} + 3 \hat {k} , \vec{b} = - \hat {i} + 2 \hat {j} + \hat {k}\] and \[\vec{c} = 3 \hat {i} + \hat {j} + 2 \hat {k}\]

Now, 

\[\vec{b} \times \vec{c} = \begin{vmatrix}\hat { i } & \hat {j} & \hat {k}\\ - 1 & 2 & 1 \\ 3 & 1 & 2\end{vmatrix} = 3\hat {  i} + 5 \hat {j} - 7 \hat {k}\]

\[\therefore \vec{a} . \left( \vec{b} \times \vec{c} \right) = \left( 2 \hat {i} + \hat {j} + 3 \hat {k} \right) . \left( 3 \hat{i} + 5 \hat {j} - 7 \hat {k} \right) = 2 \times 3 + 1 \times 5 + 3 \times \left( - 7 \right) = 6 + 5 - 21 = - 10\]

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 12 Maths
Chapter 26 Scalar Triple Product
Very Short Answers | Q 11 | Page 18
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×