Use the given vectors to find $v \cdot w$ and $v \cdot v$ .
$v = 6 i - 3 j, w = - 2 i - j$

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Final Answer: $v \cdot w = - 9$ and $v \cdot v = 45$

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Step 1 ：Given vectors are $v = 6 i - 3 j$ , $w = - 2 i - j$

Step 2 ：The dot product of two vectors can be calculated by multiplying the corresponding components of the vectors and then adding them together. For vectors in 2D, if $v = a i + b j$ and $w = c i + d j$ , then $v \cdot w = a c + b d$

Step 3 ：Substitute the given vectors into the formula, we get $v \cdot w = (6 * - 2) + (- 3 * - 1)$ and $v \cdot v = (6 * 6) + (- 3 * - 3)$

Step 4 ：Calculate the above expressions, we get $v \cdot w = - 9$ and $v \cdot v = 45$

Step 5 ：Final Answer: $v \cdot w = - 9$ and $v \cdot v = 45$

Use the given vectors to find v⋅w and v⋅v.v=6i−3j,w=−2i−j

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Use the given vectors to find $v \cdot w$ and $v \cdot v$ .
$v = 6 i - 3 j, w = - 2 i - j$