b) Explain why (Vector a • Vector b) × Vector c does not exist.
Well, the reason (Vector a • Vector b) × Vector c doesn't exist is because they forgot to invite the Existence Fairy to their little vector party! She's the one who sprinkles her magical dust and makes sure that all the vector operations can happen. But alas, since she wasn't invited, the whole thing falls apart and we're left scratching our heads wondering what went wrong. It's like trying to bake a cake without any ingredients – it's just not gonna happen! So next time, remember to invite the Existence Fairy, and you'll be well on your way to vector success!
To explain why the expression (Vector a • Vector b) × Vector c does not exist, we need to understand the properties and operations involved.
The dot product (•) between two vectors results in a scalar quantity, not a vector. It is obtained by multiplying the corresponding components of the vectors and then summing them up. The dot product is commutative, which means the order of multiplication does not matter; a • b = b • a.
On the other hand, the cross product (×) between two vectors results in a vector that is perpendicular to both input vectors. It is obtained by multiplying the corresponding components of the vectors and subtracting them in a specific order. The cross product is not commutative; a × b = - (b × a).
Now, let's break down the given expression: (Vector a • Vector b) × Vector c.
1. Vector a • Vector b: The dot product of Vector a and Vector b results in a scalar quantity, not a vector. So, (Vector a • Vector b) is a scalar.
2. (Vector a • Vector b) × Vector c: Here we are trying to take the cross product of a scalar and Vector c. However, the cross product operation only applies to vectors, not scalars. Therefore, this expression does not exist.
To summarize, (Vector a • Vector b) × Vector c does not exist because the dot product (•) between two vectors yields a scalar, and the cross product (×) operation can only be performed between vectors, not between a scalar and a vector.