CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Let $$u, v$$ and $$w$$ be such that $$\left| u \right| =1, \left| v \right| =3$$ and $$\left| w \right| =2$$. If the projection of $$v$$ along $$u$$ is equal to that of $$w$$ along $$u$$ and vectors $$v$$ and $$w$$ are perpendicular to each other, then $$\left| u-v+w \right| $$ equals


A
2
loader
B
7
loader
C
14
loader
D
14
loader

Solution

The correct option is D $$\sqrt { 14 } $$
Given, $$v\cdot u=w\cdot u$$ and $$v \perp w$$  $$\Rightarrow v\cdot w=0$$
Now, consider
$${ \left| u-v+w \right|  }^{ 2 }={ \left| u \right|  }^{ 2 }+{ \left| v \right|  }^{ 2 }+{ \left| w \right|  }^{ 2 }-2u\cdot v-2w\cdot v+2u\cdot w$$
                  $$=1+9+4=14$$
$$\Rightarrow \left| u-v+w \right| =\sqrt { 14 } $$ 

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image