Given overrightarrow{p} = 3 hat{i} + 2 hat{j} | vedclass

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(B) Given $\overrightarrow{p} = x \overrightarrow{a} + y \overrightarrow{b} + z \overrightarrow{c}$.Substituting the vectors,we get:$3 \hat{i} + 2 \ha

Vedclass · Accepted Answer

$\frac{1}{2}, \frac{3}{2}, \frac{5}{2}$

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(B) Given $\overrightarrow{p} = x \overrightarrow{a} + y \overrightarrow{b} + z \overrightarrow{c}$.Substituting the vectors,we get:$3 \hat{i} + 2 \hat{j} + 4 \hat{k} = x(\hat{i} + \hat{j}) + y(\hat{j} + \hat{k}) + z(\hat{i} + \hat{k})$$3 \hat{i} + 2 \hat{j} + 4 \hat{k} = (x + z) \hat{i} + (x + y) \hat{j} + (y + z) \hat{k}$Comparing the coefficients of $\hat{i}, \hat{j}, \hat{k}$ on both sides:$x + z = 3$  $(i)$$x + y = 2$  $(ii)$$y + z = 4$  $(iii)$Adding $(i), (ii),$ and $(iii)$:$2(x + y + z) = 3 + 2 + 4 = 9 \Rightarrow x + y + z = 4.5$Subtracting $(iii)$ from the sum: $x = 4.5 - 4 = 0.5 = \frac{1}{2}$Subtracting $(i)$ from the sum: $y = 4.5 - 3 = 1.5 = \frac{3}{2}$Subtracting $(ii)$ from the sum: $z = 4.5 - 2 = 2.5 = \frac{5}{2}$Thus,$x = \frac{1}{2}, y = \frac{3}{2}, z = \frac{5}{2}$.

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