The coordinates of the midpoints of the line segment joining the points (2, 3, 4) and (8, -3, 8) are
  • (10, 0, 12)
  • (5, 6, 0)
  • (6, 5, 0)
  • (5, 0, 6)
The direction cosines of the normal to the plane 2x – 3y – 6z – 3 = 0 are
  • \(\frac{2}{7}\), \(\frac{-3}{7}\), \(\frac{-6}{7}\)
  • \(\frac{2}{7}\), \(\frac{3}{7}\), \(\frac{6}{7}\)
  • \(\frac{-2}{7}\), \(\frac{-3}{7}\), \(\frac{-6}{7}\)
  • None of these
If 2x + 5y – 6z + 3 = 0 be the equation of the plane, then the equation of any plane parallel to the given plane is
  • 3x + 5y – 6z + 3 = 0
  • 2x – 5y – 6z + 3 = 0
  • 2x + 5y – 6z + k = 0
  • None of these
(2, – 3, – 1) 2x – 3y + 6z + 7 = 0
  • 4
  • 3
  • 2
  • \(\frac{1}{5}\)
The length of the ⊥
  • 0
  • 2√3
  • \(\frac{2}{3}\)
  • 2
The shortest distance between the lines \(\vec{r}\) = \(\vec{a}\) + k\(\vec{b}\) and r = \(\vec{a}\) + l\(\vec{c}\) is (\(\vec{b}\) and \(\vec{c}\) are non-collinear)
  • 0
  • |\(\vec{b}\).\(\vec{c}\)|
  • \(\frac{|\vec{b}×\vec{c}|}{|\vec {a}|}\)
  • \(\frac{|\vec{b}.\vec{c}|}{|\vec {a}|}\)
The equation xy = 0 in three dimensional space is represented by
  • a plane
  • two plane are right angles
  • a pair of parallel planes
  • a pair of st. line
How many lines through the origin in make equal angles with the coordinate axis?
  • 1
  • 4
  • 8
  • 2
The direction cosines of the line joining (1, -1, 1) and (-1, 1, 1) are
  • 2, -2, 0
  • 1, -1, 0
  • \(\frac{1}{√2}\), – \(\frac{1}{√2}\)
  • None of these
The equation x² – x – 2 = 0 in three dimensional space is represented by
  • A pair of parallel planes
  • A pair of straight lines
  • A pair of perpendicular plane
  • None of these
The distance of the point (-3, 4, 5) from the origin
  • 50
  • 5√2
  • 6
  • None of these
The direction ratios of a line are 1,3,5 then its direction cosines are
  • \(\frac{1}{\sqrt{35}}\), \(\frac{3}{\sqrt{35}}\), \(\frac{5}{\sqrt{35}}\)
  • \(\frac{1}{9}\), \(\frac{1}{3}\), \(\frac{5}{9}\)
  • \(\frac{5}{\sqrt{35}}\), \(\frac{3}{\sqrt{35}}\), \(\frac{1}{\sqrt{35}}\)
  • None of these
The direction ratios of the normal to the plane 7x + 4y – 2z + 5 = 0 are
  • 7, 4,-2
The direction ratios of the line of intersection of the planes 3x + 2y – z = 5 and x – y + 2z = 3 are
  • 3, 2, -1
  • -3, 7, 5
  • 1, -1, 2
  • – 11, 4, -5
The lines of intersection of the planes \(\vec{r}\)(3\(\hat{i}\) – \(\hat{j}\) + \(\hat{k}\)) = 1 and \(\vec{r}\)(\(\hat{i}\) +4\(\hat{j}\) – 2\(\hat{k}\)) = 2 is parallel to the vector
  • 2\(\hat{i}\) + 7\(\hat{j}\) + 13\(\hat{k}\)
  • -2\(\hat{i}\) – 7\(\hat{j}\) – 13\(\hat{k}\)
  • 2\(\hat{i}\) – 7\(\hat{j}\) + 13\(\hat{i}\)
The equation of the plane through the origin and parallel to the plane 3x – 4y + 5z + 6 = 0
  • 3x – 4y – 5z – 6 = 0
  • 3x – 4y + 5z + 6 = 0
  • 3x – 4y + 5z = 0
  • 3x + 4y – 5z + 6 = 0
The locus of xy + yz = 0 is
  • A pair of st. lines
  • A pair of parallel lines
  • A pair of parallel planes
  • A pair of perpendicular planes
The plane x + y = 0
  • is parallel to z-axis
  • is perpendicular to z-axis
  • passes through z-axis
  • None of these
If α, β, γ are the angle which a half ray makes with the positive directions of the axis then sin²α + sin²β + sin²γ =
  • 1
  • 2
  • 0
  • -1
If a line makes angles α, β, γ with the axis then cos 2α + cos 2β + cos 2γ =
  • -2
  • -1
  • 1
  • 2
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