A) \[{{30}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{60}^{o}}\]
D) \[{{90}^{o}}\]
Correct Answer: B
Solution :
Given, \[\mathbf{\vec{A}}=-\mathbf{\hat{i}}+2\mathbf{\hat{j}}-3\mathbf{\hat{k}}\] \[\mathbf{\vec{B}}=4\mathbf{\hat{i}}-2\mathbf{\hat{j}}+6\mathbf{\hat{k}}\] Let angle made by\[(\mathbf{\vec{A}}+\mathbf{\vec{B}})\] with \[x-\]axis is\[\theta \]. \[\cos \theta =\frac{(\mathbf{\vec{A}}+\mathbf{\vec{B}})\cdot \mathbf{\hat{i}}}{|\mathbf{\vec{A}}+\mathbf{\vec{B}}|\cdot |\mathbf{\hat{i}}|}=\frac{(3\mathbf{\hat{i}}+3\mathbf{\hat{k}})\cdot i}{\sqrt{9+9}\cdot 1}\] \[=\frac{3}{3\sqrt{2}}=\frac{1}{\sqrt{2}}\] \[\therefore \] \[\theta ={{45}^{o}}\]
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