Consider a vector A that lies in x y-plane. If Ax and Ay are the magnitudes of its x and y-components respectively, then the correct representation of A can be given by

Question

Consider a vector A that lies in x y-plane. If Ax and Ay are the magnitudes of its x and y-components respectively, then the correct representation of A can be given by (A)  (B)  (C)  (D) None of these

Tardigrade Admin · Accepted Answer

Vector along X-axis ( x-component) =Ax hat i =| A | cos θ hat i =A cos θ hat i Vector along Y - axis ( y-component) =Ay hat j =| A | sin θ hat j =A sin θ hat j This can be shown as

Q. Consider a vector $A$ that lies in $x y$ -plane. If $A_{x}$ and $A_{y}$ are the magnitudes of its $x$ and $y$ -components respectively, then the correct representation of $A$ can be given by

None of these

Vector along $X$ -axis ( $x$ -component)
$= A_{x} \hat{i} = ∣ A ∣ cos θ \hat{i} = A cos θ \hat{i}$
Vector along $Y$ - axis ( $y$ -component)
$= A_{y} \hat{j} = ∣ A ∣ sin θ \hat{j} = A sin θ \hat{j}$
This can be shown as

Q. Consider a vector A that lies in xy-plane. If Ax​ and Ay​ are the magnitudes of its x and y-components respectively, then the correct representation of A can be given by

None of these

Vector along X-axis ( x-component) =Ax​i^=∣A∣cosθi^=Acosθi^ Vector along Y - axis ( y-component) =Ay​j^​=∣A∣sinθj^​=Asinθj^​ This can be shown as

Q. Consider a vector $A$ that lies in $x y$ -plane. If $A_{x}$ and $A_{y}$ are the magnitudes of its $x$ and $y$ -components respectively, then the correct representation of $A$ can be given by

Vector along $X$ -axis ( $x$ -component)
$= A_{x} \hat{i} = ∣ A ∣ cos θ \hat{i} = A cos θ \hat{i}$
Vector along $Y$ - axis ( $y$ -component)
$= A_{y} \hat{j} = ∣ A ∣ sin θ \hat{j} = A sin θ \hat{j}$
This can be shown as