Questions in vectors

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The vector projection of a vector $3\hat i + 4\hat k$on y-axis is
Position of a particle in a rectangular-co-ordinate system is (3, 2, 5). Then its position vector will be
If a particle moves from point P (2,3,5) to point Q (3,4,5). Its displacement vector be
A force of 5 N acts on a particle along a direction making an angle of $60^o$ with vertical. Its vertical component be
If $A = 3\hat i + 4\hat j$ and $B = 7\hat i + 24\hat j,$the vector having the same magnitude as B and parallel to A is
Vector$\overrightarrow A $ makes equal angles with x, y and z axis. Value of its components (in terms of magnitude of $\overrightarrow A $) will be
If $\overrightarrow A = 2\hat i + 4\hat j - 5\hat k$ the direction of cosines of the vector $\overrightarrow A $ are
The vector that must be added to the vector $\hat i - 3\hat j + 2\hat k$ and $3\hat i + 6\hat j - 7\hat k$ so that the resultant vector is a unit vector along the y-axis is
How many minimum number of coplanar vectors having different magnitudes can be added to give zero resultant
A hall has the dimensions $10\,m \times 12\,m \times 14\,m.$A fly starting at one corner ends up at a diametrically opposite corner. What is the magnitude of its displacement

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