Question

If vector A and B are two non collinear unit vectors and if |A+B|=, then find the value of (A-B).(2A+B)



Please help! :O

Answer 1

Answer:

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Answer 2

Answer:

$(\hat A -\hat B).(2\hat A+\hat B)$ $= \frac{1}{2}$

Explanation:

Here, $\hat{A}$ and $\hat{B}$ are two non collinear unit vectors.

and     $| \hat{A} + \hat{B}| = \sqrt{3}$   ......................................................(i)

Squaring both sides of above equation (i),

      →  $\hat A^2 + \hat B^2 +2 |\hat A|.|\hat B| Cos\theta =3$

      → 1 + 1 + 2 .1.1.$Cos\theta$ = 3     [∵ the magnitude of unit vector is equal to 1]

      → $Cos\theta$ = 1/2

Now,    $(\hat A -\hat B).(2\hat A+\hat B)$

          $= 2\hat A. \hat A \ + \hat A .\hat B -2 \hat A .\hat B-\hat B.\hat B$         $[ using ,\hat A . \hat B = |\hat A||\hat B|Cos\theta ]$

          $= 2 - \frac{1}{2} -1$

          $= \frac{1}{2}$     [Ans]