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Chapter 6: Problem 29

Use the dot product to determine whether v and w are orthogonal. $$\mathbf{v}=3 \mathbf{i}, \quad \mathbf{w}=-4 \mathbf{i}$$

Short Answer

Expert verified
The vectors v and w are not orthogonal.

Step by step solution

01

Calculate Dot Product

First calculate the dot product of the two vectors. The dot product of two vectors \( \mathbf{a} = a_1 \mathbf{i} \) and \( \mathbf{b} = b_1 \mathbf{i} \) is given by \( \mathbf{a}.\mathbf{b}= a_1*b_1 \). In this case, \( \mathbf{v}. \mathbf{w} = 3*-4.\mathbf{i}.\mathbf{i} = -12 \)
02

Check if dot product equals zero

After computing the dot product, check if it equals zero. If it is zero, then the two vectors are orthogonal. In this case, the dot product is -12, not zero.
03

Conclusion

Since the dot product is not zero, v and w are not orthogonal.

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