Maths · Scalar and vector products
Given and Find the value of \cdot\left(\boldsymbol{3} \overrightarrow{\boldsymbo
Given \( \left|\overrightarrow{\boldsymbol{A}}_{1}\right|=2,\left|\overrightarrow{\boldsymbol{A}}_{2}\right|=\overrightarrow{\mathbf{3}} \) and \( \left|\vec{A}_{1}+\vec{A}_{2}\right|=3 . \) Find the value of \( \left(\overrightarrow{\boldsymbol{A}}_{1}+\mathbf{2} \overrightarrow{\boldsymbol{A}}_{2}\right) \cdot\left(\boldsymbol{3} \overrightarrow{\boldsymbol{A}}_{1}-\boldsymbol{4} \boldsymbol{\vec { A }}_{2}\right) \)
- A. -64
- B. 60
- C. -60
- D. 64
Step-by-step solution
Given |A1|=2, |A2|=3, |A1+A2|=3. Compute (A1+2A2)·(3A1-4A2) = 3|A1|^2 + 2A1·A2 -8|A2|^2. From |A1+A2|^2 = |A1|^2+|A2|^2+2A1·A2 = 9, get 2A1·A2 = -4, so A1·A2 = -2. Then expression = 3(4) + 2(-2) -8(9) = 12 -4 -72 = -64.
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