A) \[[\overset{\to }{\mathop{\mathbf{a}}}\,\overset{\to }{\mathop{\mathbf{b}}}\,\overset{\to }{\mathop{\mathbf{c}}}\,]\]
B) \[3[\overset{\to }{\mathop{\mathbf{a}}}\,\overset{\to }{\mathop{\mathbf{b}}}\,\overset{\to }{\mathop{\mathbf{c}}}\,]\]
C) \[0\]
D) \[2[\overset{\to }{\mathop{\mathbf{a}}}\,\overset{\to }{\mathop{\mathbf{b}}}\,\overset{\to }{\mathop{\mathbf{c}}}\,]\]
Correct Answer: C
Solution :
\[\therefore \]\[\overset{\to }{\mathop{\mathbf{a}}}\,\cdot (\overset{\to }{\mathop{\mathbf{b}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,)\times (\overset{\to }{\mathop{\mathbf{a}}}\,+\overset{\to }{\mathop{\mathbf{b}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,)\] \[=\overset{\to }{\mathop{\mathbf{a}}}\,\cdot [\overset{\to }{\mathop{\mathbf{b}}}\,\times \overset{\to }{\mathop{\mathbf{a}}}\,+\overset{\to }{\mathop{\mathbf{b}}}\,\times \overset{\to }{\mathop{\mathbf{b}}}\,+\overset{\to }{\mathop{\mathbf{b}}}\,\times \overset{\to }{\mathop{\mathbf{c}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,\times \overset{\to }{\mathop{\mathbf{a}}}\,\] \[+\overset{\to }{\mathop{\mathbf{c}}}\,\times \overset{\to }{\mathop{\mathbf{b}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,\times \overset{\to }{\mathop{\mathbf{c}}}\,]\] \[=[\overset{\to }{\mathop{\mathbf{a}}}\,\overset{\to }{\mathop{\mathbf{b}}}\,\overset{\to }{\mathop{\mathbf{c}}}\,]+[\overset{\to }{\mathop{\mathbf{a}}}\,\overset{\to }{\mathop{\mathbf{b}}}\,\overset{\to }{\mathop{\mathbf{b}}}\,]+[\overset{\to }{\mathop{\mathbf{a}}}\,\overset{\to }{\mathop{\mathbf{b}}}\,\overset{\to }{\mathop{\mathbf{c}}}\,]+[\overset{\to }{\mathop{\mathbf{a}}}\,\overset{\to }{\mathop{\mathbf{c}}}\,\overset{\to }{\mathop{\mathbf{a}}}\,]\] \[+[\overset{\to }{\mathop{\mathbf{a}}}\,\overset{\to }{\mathop{\mathbf{c}}}\,\overset{\to }{\mathop{\mathbf{b}}}\,]+[\overset{\to }{\mathop{\mathbf{a}}}\,\overset{\to }{\mathop{\mathbf{c}}}\,\overset{\to }{\mathop{\mathbf{c}}}\,]\] \[=0+0+[\overset{\to }{\mathop{\mathbf{a}}}\,\overset{\to }{\mathop{\mathbf{b}}}\,\overset{\to }{\mathop{\mathbf{c}}}\,]+0-[\overset{\to }{\mathop{\mathbf{a}}}\,\overset{\to }{\mathop{\mathbf{b}}}\,\overset{\to }{\mathop{\mathbf{c}}}\,]+0\] \[=0\]
You need to login to perform this action.
You will be redirected in
3 sec
