Vector Algebra - I Book Back Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 25
    5 x 1 = 5
  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. 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)

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

  3. 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.

  4. If\(\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\)are the position vectors of three collinear points, then which of the following is true?

    (a)

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

    (b)

    \(2\overrightarrow{a}=\overrightarrow{b}+\overrightarrow{c}\)

    (c)

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

    (d)

    \(4\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0\)

  5. If \(\lambda \hat{i}+2\lambda \hat{j}+2\lambda \hat{k}\) is a unit vector, then the value of \(\lambda\)is

    (a)

    \({1\over3}\)

    (b)

    \({1\over4}\)

    (c)

    \({1\over9}\)

    (d)

    \({1\over2}\)

  6. 3 x 2 = 6
  7. Represent graphically the displacement of 80km, 60° south of west

  8. Find the direction cosines of a vector whose direction ratios are 2, 3, - 6.

  9. Find the direction cosines of \(\overrightarrow{AB},\)where A is (2, 3, 1) and B is (3, - 1, 2).

  10. 3 x 3 = 9
  11. Show that the points whose position vectors are 2\(\hat{i}\)+ 3\(\hat{j}\)− 5\(\hat{k}\), 3\(\hat{i}\)+ \(\hat{j}\)− 2\(\hat{k}\) and, 6\(\hat{i}\)− 5 \(\hat{j}\)+ 7\(\hat{k}\) are collinear

  12. If \(\overrightarrow{a},\overrightarrow{b},\)and \(\overrightarrow{c}\) are three unit vectors satisfying  \(\overrightarrow{a}-\sqrt{3}\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}\)  then find the angle between \(\overrightarrow{a}\) and \(\overrightarrow{c}\) .

  13. Find the unit vector in the direction of the vector \(\overrightarrow { a } -2\overrightarrow { b } +3\overrightarrow { c } \) if \(\overrightarrow { a } =\hat { i } +\hat { j } ,\overrightarrow { b } =\hat { j } +\hat { k } \) and \(\overrightarrow { c } =\hat { i } +\hat { k } \) .

  14. 1 x 5 = 5
  15. If \(\overrightarrow{a},\overrightarrow{b}\)are unit vectors and \(\theta\) is the angle between them, show that \(sin {\theta \over 2}={1\over2}|\overrightarrow{a}-\overrightarrow{b}|\)

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