91影视

The following information is given.

$\stackrel{鈫�}{d_1}+\stackrel{鈫�}{d_2}=5\stackrel{鈫�}{d_3}$ (i)

$\stackrel{鈫�}{d_1}-\stackrel{鈫�}{d_2}=3\stackrel{鈫�}{d_3}$ (ii)

$\stackrel{鈫�}{d_3}=2\hat{i}+4\hat{j}$ (iii)

Use the vector addition and vector subtraction laws to calculate the values of vector$\stackrel{\mathbf{鈫�}}{{\mathbf{d}}_{\mathbf{1}}}$and $\stackrel{\mathbf{鈫�}}{{\mathbf{d}}_2}$.

To calculate the values of vectors, add equations (i) and (ii) as follows:

$\begin{array}{rcl}\left(\stackrel{鈫�}{d_1}+\stackrel{鈫�}{d_2}\right)+\left(\stackrel{鈫�}{d_1}-\stackrel{鈫�}{d_2}\right)& =& 5\stackrel{鈫�}{d_3}+3\stackrel{鈫�}{d_3}\\ & =& 8\stackrel{鈫�}{d_3}\\ 2\stackrel{鈫�}{d_1}& =& 8\stackrel{鈫�}{d_3}\\ \stackrel{鈫�}{d_1}& =& 4\stackrel{鈫�}{d_3}\\ & & \end{array}$

From equation (iii),

$\stackrel{鈫�}{d_1}+\stackrel{鈫�}{d_2}=5\stackrel{鈫�}{d_3}$

Substituting the value of $\stackrel{鈫�}{d_1}$, we get

$\stackrel{鈫�}{d_2}=\stackrel{鈫�}{d_3}$

Therefore, the vector in $\stackrel{鈫�}{d_2}$unit vector notation is,

$\stackrel{鈫�}{d_2}=2\hat{i}+4\hat{j}$

Now, use the value of $\stackrel{鈫�}{d_2}$to calculate the $\stackrel{鈫�}{d_1}$

$\begin{array}{rcl}\stackrel{鈫�}{d_1}& =& 4脳\stackrel{鈫�}{d_3}\\ & =& 4脳\left(2\hat{i}+4\hat{j}\right)\\ & =& 8\hat{i}+16\hat{j}\\ & & \end{array}$

Therefore, $\stackrel{鈫�}{d_1}=8\hat{i}+16\hat{j}$androle="math" localid="1660886521162" $\stackrel{鈫�}{d_2}=2\hat{i}+4\hat{j}$