OnlineCBT
Physics · MOTION IN A PLANE
हिन्दीGiven two vectors \( \mathbf{A} = 2\hat{\mathbf{i}} + 3\hat{\mathbf{j}} - \hat{\mathbf{k}} \) and \( \mathbf{B} = \hat{\mathbf{i}} - 2\hat{\mathbf{j}} + 2\hat{\mathbf{k}} \). Find a unit vector parallel to the linear combination vector \( \mathbf{C} = 2\mathbf{A} - 3\mathbf{B} \).
Correct answer · Option 2
\( \frac{\hat{\mathbf{i}} + 12\hat{\mathbf{j}} - 8\hat{\mathbf{k}}}{\sqrt{209}} \)
Explanation
\( \mathbf{C} = 2(2\hat{\mathbf{i}} + 3\hat{\mathbf{j}} - \hat{\mathbf{k}}) - 3(\hat{\mathbf{i}} - 2\hat{\mathbf{j}} + 2\hat{\mathbf{k}}) = \hat{\mathbf{i}} + 12\hat{\mathbf{j}} - 8\hat{\mathbf{k}} \). Its magnitude is \( |\mathbf{C}| = \sqrt{1^2 + 12^2 + (-8)^2} = \sqrt{209} \). The unit vector is \( \frac{\hat{\mathbf{i}} + 12\hat{\mathbf{j}} - 8\hat{\mathbf{k}}}{\sqrt{209}} \).
