Questions in vectors

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A particle has displacement of 12 m towards east and 5 m towards north then 6 m vertically upward. The sum of these displacements is
The three vectors $\overrightarrow A = 3\hat i - 2\hat j + \hat k,\,\,\overrightarrow B = \hat i - 3\hat j + 5\hat k$ and $\overrightarrow C = 2\hat i + \hat j - 4\hat k$ form
Let $\overrightarrow C = \overrightarrow A + \overrightarrow B $ then
The value of the sum of two vectors $\overrightarrow A $ and $\overrightarrow B $ with $\theta $ as the angle between them is
Following sets of three forces act on a body. Whose resultant cannot be zero
When three forces of 50 N, 30 N and 15 N act on a body, then the body is
The sum of two forces acting at a point is 16 N. If the resultant force is 8 N and its direction is perpendicular to minimum force then the forces are
If vectors P, Q and R have magnitude 5, 12 and 13 units and $\overrightarrow P + \overrightarrow Q = \overrightarrow R ,$ the angle between Q and R is
The resultant of two vectors A and B is perpendicular to the vector A and its magnitude is equal to half the magnitude of vector B. The angle between A and B is
What vector must be added to the two vectors $\hat i - 2\hat j + 2\hat k$ and $2\hat i + \hat j - \hat k,$ so that the resultant may be a unit vector along x-axis

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