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#### Pranav

##### Well-known member

- Nov 4, 2013

- 428

**Problem:**

Find $\vec{v_1}$,$\vec{v_2}$ and $\vec{v_3}$ given that:

$$\vec{v_1}\cdot \vec{v_1}=4$$

$$\vec{v_1}\cdot \vec{v_2}=-2$$

$$\vec{v_1}\cdot \vec{v_3}=6$$

$$\vec{v_2}\cdot \vec{v_2}=2$$

$$\vec{v_2}\cdot \vec{v_3}=-5$$

$$\vec{v_3}\cdot \vec{v_3}=29$$

**Attempt:**

Assuming the vector $\vec{v_i}$ as $x_i \hat{i}+y_i \hat{j}+z_i \hat{k}$ is definitely not a good idea.

I am really clueless on how to tackle this problem. I can see that adding the second and fourth equation gives $\vec{v_2}\cdot (\vec{v_1}+\vec{v_2})=0$. This means that $\vec{v_1}$ is perpendicular to $\vec{v_1}+\vec{v_2}$ but I am not sure if this helps. I need a few hints to begin with.

Any help is appreciated. Thanks!