Question
What would be the effect on a vector if all its components are reversed in direction?
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Answer
Consider a vector $\vec{\text{F}}.$ $\vec{\text{F}}=\text{F}_\text{x}\hat{\text{i}}+\text{F}_\text{y}\hat{\text{j}}+\text{F}_\text{z}\hat{\text{k}}$ When x, y and z components are reversed, we get $\text{F}_\text{x}(-\hat{\text{i}})+\text{F}_\text{y}(-\hat{\text{j}})+\text{F}_\text{z}(-\hat{\text{k}})$ $-[\text{F}_\text{x}\hat{\text{i}}+\text{F}_\text{y}\hat{\text{j}}+\text{F}_\text{z}\hat{\text{k}}]=-\vec{\text{F}}$ Therefore, the vector itself is reversed.
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