A) \[14\]
B) \[\sqrt{7}\]
C) \[\sqrt{14}\]
D) 2
Correct Answer: C
Solution :
| Projection of \[\vec{v}\] along \[\vec{u}=\frac{\text{\vec{v}}\text{.\vec{u}}}{|\text{\vec{u} }\!\!|\!\!\text{ }}=\frac{\text{\vec{v}}\text{.\vec{u}}}{1}\] |
| Projection of \[\vec{w}\] along \[\vec{u}=\frac{\vec{w}.\vec{u}}{|\vec{u}|}=\frac{\vec{w}.\vec{u}}{1}\] |
| Given \[\text{\vec{v}}\text{.\vec{u}=\vec{w}}\text{.\vec{u}}\] .??(1) |
| Also, \[\text{\vec{v}}\text{.\vec{w}=0}\] ??.(2) |
| Now \[|\vec{u}-\text{\vec{v} + \vec{w}}{{\text{ }\!\!|\!\!\text{ }}^{2}}\] |
| \[=|\vec{u}{{|}^{2}}+|\text{\vec{v}}{{\text{ }\!\!|\!\!\text{ }}^{2}}+|\vec{w}{{|}^{2}}-2\vec{u}.\text{\vec{v} }-2\text{\vec{v}}\text{.\vec{w}+2\vec{u}}\text{.\vec{w}}\] |
| \[=1+4+9+0\][From (1) and (2)] |
| \[=14\] |
| \[\therefore \,\,\,|\vec{u}-\text{\vec{v}+\vec{w} }\!\!|\!\!\text{ =}\sqrt{14}\] |
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