The vectors bar{a} and bar{b} are not perpend | vedclass

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(B) Given that $\overline{a}$ and $\overline{b}$ are not perpendicular,so $\overline{a} \cdot \overline{b} 
eq 0$. We are given $\overline{a} \cdot \

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$\overline{c} - \left(\frac{\overline{a} \cdot \overline{c}}{\overline{a} \cdot \overline{b}}\right) \overline{b}$

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(B) Given that $\overline{a}$ and $\overline{b}$ are not perpendicular,so $\overline{a} \cdot \overline{b} 
eq 0$. We are given $\overline{a} \cdot \overline{d} = 0$ and $\overline{b} 	imes \overline{c} = \overline{b} 	imes \overline{d}$. Taking the cross product with $\overline{a}$ on both sides of the equation $\overline{b} 	imes \overline{c} = \overline{b} 	imes \overline{d}$,we get: $\overline{a} 	imes (\overline{b} 	imes \overline{c}) = \overline{a} 	imes (\overline{b} 	imes \overline{d})$ Using the vector triple product formula $\overline{a} 	imes (\overline{b} 	imes \overline{c}) = (\overline{a} \cdot \overline{c}) \overline{b} - (\overline{a} \cdot \overline{b}) \overline{c}$,we have: $(\overline{a} \cdot \overline{c}) \overline{b} - (\overline{a} \cdot \overline{b}) \overline{c} = (\overline{a} \cdot \overline{d}) \overline{b} - (\overline{a} \cdot \overline{b}) \overline{d}$ Since $\overline{a} \cdot \overline{d} = 0$,the equation simplifies to: $(\overline{a} \cdot \overline{c}) \overline{b} - (\overline{a} \cdot \overline{b}) \overline{c} = 0 - (\overline{a} \cdot \overline{b}) \overline{d}$ Rearranging to solve for $\overline{d}$: $(\overline{a} \cdot \overline{b}) \overline{d} = (\overline{a} \cdot \overline{b}) \overline{c} - (\overline{a} \cdot \overline{c}) \overline{b}$ Dividing by $(\overline{a} \cdot \overline{b})$: $\overline{d} = \overline{c} - \left(\frac{\overline{a} \cdot \overline{c}}{\overline{a} \cdot \overline{b}}ight) \overline{b}$

The vectors $\bar{a}$ and $\bar{b}$ are not perpendicular and $\overline{c}$ and $\overline{d}$ are two vectors satisfying $\overline{b} \times \overline{c} = \overline{b} \times \overline{d}$ and $\overline{a} \cdot \overline{d} = 0$. Then the vector $\overline{d}$ is equal to:

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