If - - and k-are the unit vectors along positive direction of x- y and z axes respectively and r-a-b-ck-then the component of r-along z axis is b-TrueFalse

The correct option is B FalseWe know that any vector r⃗ can be uniquely expressed as r⃗ =xî+yĵ +zk̂ where î,ĵ and k̂ constitute the orthogonal system of unit v ...

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Byju's Answer

Standard X

Mathematics

Orthogonal System of Vectors

If î, ĵ and k...

Question

If $^i,^j$ and $^k$ are the unit vectors along positive direction of x, y and z axes respectively and $\to r = a^i + b^j + c^k$ then the component of $\to r$ along z axis is b.

True

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False

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Solution

The correct option is B False
We know that any vector $\to r$ can be uniquely expressed as $\to r = x^i + y^j + z^k$ where $^i,^j$ and $^k$ constitute the orthogonal system of unit vectors. Here the vector $\to r$ is expressed as a sum of its components along x, y and z axes.
Coefficient of $^i$ = component in x – direction
Coefficient of $^j$ = component in y – direction
Coefficient of $^k$ = component in z – direction
So in the vector $\to r = a^i + b^j + c^k$ the component along z axis will be the coefficient of $^k$ i.e., c

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If ^i,^j and ^k are the unit vectors along positive direction of x, y and z axes respectively and →r=a^i+b^j+c^k then the component of →r along z axis is b.

If $^i,^j$ and $^k$ are the unit vectors along positive direction of x, y and z axes respectively and $\to r = a^i + b^j + c^k$ then the component of $\to r$ along z axis is b.