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Mathematics Test - 21
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  • Question 1/10
    5 / -1
    Find a unit vector parallel to the vector -2î + 3ĵ.
  • Question 2/10
    5 / -1
    The direction cosines of the line that makes equal angles with three axes in a space are
  • Question 3/10
    5 / -1
    If \(\vec r = ​​\vec A_1 + \lambda \vec B_1 \) and \(\vec r = ​​\vec A_2 + \lambda \vec B_2 \) are intersecting lines then which of the following is correct?
  • Question 4/10
    5 / -1
    There are 2 vectors \(\rm \vec a\)= i + 2j + k and \(\rm \vec b\) = -i + j - 3k. Find the projection of \(\rm \vec a\) on \(\rm \vec b\)
  • Question 5/10
    5 / -1
    If a, b, c are non-coplanar then find the value of 2[a b c] + [b a c] =
  • Question 6/10
    5 / -1
    If the straight line \(\frac{x-x_0}{l}=\frac{y-y_0}{m}=\frac{z-z_0}{n}\) is parallel to the plane ax + by + cz + d = 0, then which one of the following is correct?
  • Question 7/10
    5 / -1
    If \(|\vec a|\) = 3, \(\left| {\vec b} \right| = 4\) and \(\left| {\vec a - \vec b} \right| = 5,\) then what is the value of \(\left| {\vec a + \vec b} \right|\)?
  • Question 8/10
    5 / -1

    Find the value of k for which the line through the points (2, 4, 8) and (1, 2, 4) is parallel to the line through the points (3, 6, k) and (1, 2, 1) ?

  • Question 9/10
    5 / -1
    If the vectors \(\widehat i + 2\widehat j + 3\widehat k\), \(λ \widehat i + 4\widehat j + 7\widehat k\), \(- 3\widehat i - 2\widehat j - 5\widehat k\) are collinear if λ equals
  • Question 10/10
    5 / -1
    In what ratio is the line segment joining the point (−2, −3) and (3, 7) divided by y-axis ?
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