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Can a vector have zero magnitude if one of its components is not zero?

Can a vector have zero magnitude if one of its components is not zero?

Grade:upto college level

3 Answers

Deepak Patra
askIITians Faculty 471 Points
9 years ago
No, a vector cannot have zero magnitude if one of its components is not zero.
Consider a vector\overrightarrow{b} = b_{x}\widehat{i}+b_{y}\widehat{j}+b_{z}\widehat{k} such that its magnitude is:
\left | \overrightarrow{b} \right | = \sqrt{b_{x}^{2}+b_{y}^{2}+b_{z}^{2}}
It can be seen from this equation that if any ofb_{x}, b_{y} orb_{z} is non-zero, the magnitude of vector\overrightarrow{b} will also be non-zero.
Khwaga Jenay
32 Points
7 years ago
Can the two vector having different magnitude to be combined to give a zero resultant and can three vector
ankit singh
askIITians Faculty 614 Points
3 years ago
No, a vector cannot have zero magnitude if one of its components is not zero. The Brainliest Answer! The magnitude of a vector is computed as the sum of squares of its elements. ... However, if those elements are complex numbers, for example, then it is possible that the vector has zero magn

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