Vector Algebra - I One Mark Question

11th Standard

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Maths

Time : 00:30:00 Hrs
Total Marks : 10
    10 x 1 = 10
  1. The value of \(\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{DA}+\overrightarrow{CD}\) is

    (a)

    \(\overrightarrow{AD}\)

    (b)

    \(\overrightarrow{CA}\)

    (c)

    \(\overrightarrow{0}\)

    (d)

    \(-\overrightarrow{AD}\)

  2. If \(\overrightarrow{a}+2\overrightarrow{b}\) and \(3\overrightarrow{a}+m\overrightarrow{b}\) are parallel, then the value of m is

    (a)

    3

    (b)

    \(1\over3\)

    (c)

    6

    (d)

    \(1\over6\)

  3. The unit vector parallel to the resultant of the vectors \(\hat{i}+\hat{j}-\hat{k}\) and\(\hat{i}-2\hat{j}+\hat{k}\) is

    (a)

    \({\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}\)

    (b)

    \({2\hat{i}+\hat{j}\over\sqrt{5}}\)

    (c)

    \({2\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}\)

    (d)

    \({2\hat{i}-\hat{j}\over\sqrt{5}}\)

  4. A vector \(\overrightarrow{OP}\) makes 60° and 45° with the positive direction of the x and y axes respectively.  Then the angle between \(\overrightarrow{OP}\)and the z-axis is

    (a)

    45°

    (b)

    60°

    (c)

    90°

    (d)

    30°

  5. If \(\overrightarrow{BA}=3\hat{i}+2\hat{j}+\hat{k}\) and the position vector of is \(\hat{i}+3\hat{j}-\hat{k}\) ,then the position vector A is

    (a)

    \(4\hat{i}+2\hat{j}+\hat{k}\)

    (b)

    \(4\hat{i}+5\hat{j}\)

    (c)

    \(4\hat{i}\)

    (d)

    \(-4\hat{i}\)

  6. A vector makes equal angle with the positive direction of the coordinate axes. Then each angle is equal to

    (a)

    \(cos^{-1}({1\over 3})\)

    (b)

    \(cos^{-1}({2\over 3})\)

    (c)

    \(cos^{-1}({1\over\sqrt 3})\)

    (d)

    \(cos^{-1}({2\over\sqrt 3})\)

  7. The vectors \(\overrightarrow{a}-\overrightarrow{b},\overrightarrow{b}-\overrightarrow{c},\overrightarrow{c}-\overrightarrow{a}\) are

    (a)

    parallel to each other

    (b)

    unit vectors

    (c)

    mutually perpendicular vectors

    (d)

    coplanar vectors.

  8. If ABCD is a parallelogram, then \(\overrightarrow{AB}+\overrightarrow{AD}+\overrightarrow{CB}+\overrightarrow{CD}\) is equal to 

    (a)

    \(2(\overrightarrow{AB}+\overrightarrow{AD})\)

    (b)

    \(4\overrightarrow{AC}\)

    (c)

    \(4\overrightarrow{BD}\)

    (d)

    \(\overrightarrow{0}\)

  9. One of the diagonals of parallelogram ABCD with \(\overrightarrow{a}\) and \(\overrightarrow{b}\) as adjacent sides is \(\overrightarrow{a}+\overrightarrow{b}\)The other diagonal \(\overrightarrow{BD}\) is

    (a)

    \(\overrightarrow{a}-\overrightarrow{b}\)

    (b)

    \(\overrightarrow{b}-\overrightarrow{a}\)

    (c)

    \(\overrightarrow{a}+\overrightarrow{b}\)

    (d)

    \(\overrightarrow{a}+\overrightarrow{b}\over 3\)

  10. If \(\overrightarrow{a},\overrightarrow{b}\) are the position vectors A and B, then which one of the following points whose position vector lies on AB, is

    (a)

    \(\overrightarrow{a}+\overrightarrow{b}\)

    (b)

    \({2\overrightarrow{a}-\overrightarrow{b}\over 2}\)

    (c)

    \({2\overrightarrow{a}+\overrightarrow{b}\over 2}\)

    (d)

    \({\overrightarrow{a}-\overrightarrow{b}\over 3}\)

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