SATHEE: Vectors 3 Question 23

Vectors 3 Question 23

23. If $\vec{A}, \vec{B}, \vec{C}$ are three non-coplanar vectors, then $\frac{\vec{A} \cdot (\vec{B} \times \vec{C})}{(\vec{C} \times \vec{A}) \cdot \vec{B}} + \frac{\vec{B} \cdot (\vec{A} \times \vec{C})}{\vec{C} \cdot (\vec{A} \times \vec{B})} = \dots$

(1985, 2M)

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Answer:

Correct Answer: 23. (0)

Solution:

$\frac{\vec{A} \cdot (\vec{B} \times \vec{C})}{(\vec{C} \times \vec{A}) \cdot \vec{B}} + \frac{\vec{B} \cdot (\vec{A} \times \vec{C})}{\vec{C} \cdot (\vec{A} \times \vec{B})}$

$= \frac{[\vec{A} \vec{B} \vec{C}]}{[\vec{C} \vec{A} \vec{B}]} + \frac{[\vec{B} \vec{A} \vec{C}]}{[\vec{C} \vec{A} \vec{B}]} = \frac{[\vec{A} \vec{B} \vec{C}] - [\vec{A} \vec{B} \vec{C}]}{[\vec{C} \vec{A} \vec{B}]} = 0$

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Vectors 3 Question 23

23. If A→,B→,C→ are three non-coplanar vectors, then A→⋅(B→×C→)(C→×A→)⋅B→+B→⋅(A→×C→)C→⋅(A→×B→)=…

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23. If $\vec{A}, \vec{B}, \vec{C}$ are three non-coplanar vectors, then $\frac{\vec{A} \cdot (\vec{B} \times \vec{C})}{(\vec{C} \times \vec{A}) \cdot \vec{B}} + \frac{\vec{B} \cdot (\vec{A} \times \vec{C})}{\vec{C} \cdot (\vec{A} \times \vec{B})} = \dots$