Questions in vectors

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If $|{\overrightarrow V _1} + {\overrightarrow V _2}|\, = \,|{\overrightarrow V _1} - {\overrightarrow V _2}|$and ${V_2}$ is finite, then
A force $\overrightarrow F = (5\hat i + 3\hat j)$Newton is applied over a particle which displaces it from its origin to the point $\overrightarrow r = (2\hat i - 1\hat j)$ metres. The work done on the particle is
The angle between two vectors $ - 2\hat i + 3\hat j + \hat k$ and $\hat i + 2\hat j - 4\hat k$ is
The angle between the vectors $(\hat i + \hat j)$ and $(\hat j + \hat k)$ is
A particle moves with a velocity $6\hat i - 4\hat j + 3\hat k\,m/s$under the influence of a constant force $\overrightarrow F = 20\hat i + 15\hat j - 5\hat k\,N.\,$The instantaneous power applied to the particle is
If $\overrightarrow P .\overrightarrow Q = PQ,$then angle between $\overrightarrow P $and $\overrightarrow Q $ is
A force $\overrightarrow {\rm{F}} = 5\hat i + 6\hat j + 4\hat k$ acting on a body, produces a displacement $\overrightarrow {\rm{S}} = 6\hat i - 5\hat k.$Work done by the force is
The angle between the two vectors $\overrightarrow A = 5\hat i + 5\hat j$ and $\overrightarrow B = 5\hat i - 5\hat j$ will be
The vector $\overrightarrow P = a\hat i + a\hat j + 3\hat k$ and $\overrightarrow Q = a\hat i - 2\hat j - \hat k$ are perpendicular to each other. The positive value of a is
A body, constrained to move in the Y-direction is subjected to a force given by $\overrightarrow F = ( - 2\hat i + 15\hat j + 6\hat k)\,N.$ What is the work done by this force in moving the body a distance 10 m along the Y-axis

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