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The position vectors of three points A, B and C respectively, where   and   respectively, where . What is  equal to?

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  4. Unit vector

Answer (Detailed Solution Below)

Option 1 :
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Detailed Solution

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Calculation:

Given,

The position vectors of points A, B, and C are , , and respectively, and .

The expression to evaluate is: .

First, substitute into the equation:

.

Using the distributive property of the cross product:

.

Since and , we are left with:

.

Substitute into the expression:

.

Factor out

.

Since , the expression becomes:

.

∴ The final result is .

Hence, the correct answer is option 1. 

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