Math  /  Algebra

Question1. (i×j)k=i(j×k)(\vec{i} \times \vec{j}) \cdot \vec{k}=\vec{i} \cdot(\vec{j} \times \vec{k}).
2. If v\vec{v} and w\vec{w} are any two vectors, then v+w=v+w\|\vec{v}+\vec{w}\|=\|\vec{v}\|+\|\vec{w}\|.
3. The value of v(v×w)\vec{v} \cdot(\vec{v} \times \vec{w}) is always zero.
4. For any scalar cc and any vector v\vec{v}, we have cv=cv\|c \vec{v}\|=c\|\vec{v}\|. earn 50%50 \% partial credit for 2 - 3 correct answers. Answers Submit Answers npted this problem 2 times. corded score is 0%0 \%. empts remainina.

Studdy Solution
Analyze the fourth statement: cv=cv\|c \vec{v}\| = c \|\vec{v}\|.
- The norm of a scalar multiple of a vector is given by cv=cv\|c \vec{v}\| = |c| \|\vec{v}\|. - The statement is true only if cc is non-negative.
The statement is false for negative cc.
The correct answers are:
1. True
2. False
3. True
4. False

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