91影视

$鈥�Thegivenvectorsare,\stackrel{鈫�}{A}=5.0\widehat{i}鈭�6.3\widehat{j},\text{鈥�}\stackrel{鈫�}{A}=11.2\widehat{j}鈭�9.91\widehat{i},\text{鈥�}\stackrel{鈫�}{A}=鈭�15.0\widehat{i}+22.4\widehat{j}and\stackrel{鈫�}{B}=4\widehat{i}鈭�6\widehat{j}$

$鈥�Therelationbetweenvector\stackrel{鈫�}{A}andvector\stackrel{鈫�}{B}isgivenby\stackrel{鈫�}{A}=5.0\stackrel{鈫�}{B}$

For a given vector$\stackrel{鈫�}{A}=A_x\widehat{i}+A_y\widehat{j}$, A_x is the component in x- direction and A_y is the component in y-direction and are the unit vectors in x and y directions respectively

Part(a)

The given vector $\stackrel{鈬赌}{A}$ can be represented as,

$\stackrel{鈫�}{A}=5.0\widehat{i}鈭�6.3\widehat{j}$

The given vector can be represented in the form of $\stackrel{鈫�}{A}=A_x\widehat{i}+A_y\widehat{j}$ as,

$\stackrel{鈫�}{A}=5.0\widehat{i}+\left(鈭�6.3\right)\widehat{j}$

The components of the given vector A_x and A_y will be,

A_x = 5.0

A_y = -6.3

Thus, the component of the given vector in the x-direction is A_x = 5.0 and the component in the y-direction is A_y = -6.3 .

Part(b)

The given vector$\stackrel{鈫�}{A}$ can be represented as,

$\stackrel{鈫�}{A}=11.2\widehat{j}鈭�9.91\widehat{i}$

The given vector can be represented in the form of $\stackrel{鈫�}{A}=A_x\widehat{i}+A_y\widehat{j}$ as,

$\stackrel{鈫�}{A}=\left(鈭�9.91\right)\widehat{i}+11.2\widehat{j}$

The components of the given vector A_x and A_y can be represented as,

$\begin{array}{l}{A}_x=鈭�9.11\\ A_y=11.2\end{array}$

Thus, the component of the given vector in the x-direction is A_X = -9.11 and the component in the y-direction is A_y= 11.2

Part(c)

The given vector$\stackrel{鈫�}{A}$ can be represented as,

$\stackrel{鈫�}{A}=鈭�15.0\widehat{i}+22.4\widehat{j}$

The given vector can be represented in the form of $\stackrel{鈫�}{A}=A_x\widehat{i}+A_y\widehat{j}$ as,

$\stackrel{鈫�}{A}=\left(鈭�15.0\right)\widehat{i}+22.4\widehat{j}$

The components of the given vector A_x and A_y can be represented as,

$\begin{array}{l}{A}_x=鈭�15.0\\ A_y=22.4\end{array}$

Thus, the component of the given vector in the x-direction is A_x= -15.0 and the component in the y-direction is A_y= 22.4 .

Part(d)

The given vector $\stackrel{鈫�}{B}$ can be represented as,

$\stackrel{鈫�}{B}=4\widehat{i}鈭�6\widehat{j}$

The relation between vector $\stackrel{鈫�}{A}$and vector $\stackrel{鈫�}{B}$can be expressed as,

$\stackrel{鈫�}{A}=5.0\stackrel{鈫�}{B}$

$Substitute4\widehat{i}鈭�6\widehat{j}for\stackrel{鈫�}{B}$

$\begin{array}{c}\stackrel{鈫�}{A}=5.0\stackrel{鈫�}{B}\\ =5.0\left(4\widehat{i}鈭�6\widehat{j}\right)\\ =\left(5.0脳4\right)\widehat{i}鈭�\left(5.0脳6\right)\widehat{j}\\ =20.0\widehat{i}鈭�30.0\widehat{j}\end{array}$

The given vector can be represented in the form of $\stackrel{鈫�}{A}=A_x\widehat{i}+A_y\widehat{j}$as,

$\stackrel{鈫�}{A}=20.0\widehat{i}+\left(鈭�30.0\right)\widehat{j}$

The components of the given vector A_x and A_y can be represented as,

A_x = 20.0

A_y = -30.0

Thus, the component of the given vector in the x-direction is A_x = 20.0 and the component in the y-direction is A_y = -30.0