The point of intersection of the lines x - 53 

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 Multiple Choice QuestionsMultiple Choice Questions

41.

If a line in the space makes angle α, β and γ with the coordinate axes, then

cos2α + cos2β + cos2γ + sin2α + sin2β + sin2γ equals

  • - 1

  • 0

  • 1

  • 2


42.

Y-axis cuts the line joining the points (- 3, - 4) and (1, - 2) in the ratio

  • 1 : 3

  • 2 : 3

  • 3 : 1

  • 3 : 2


43.

If the points (1, 1), (- 1, - 1), - 3, 3 are the vertices of a triangle, then this triangle is

  • a right-angled triangle

  • an isosceles triangle

  • an equilateral triangle

  • None of the above


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44.

The point of intersection of the lines x - 53 = y - 7- 1 = z + 21 and x + 3- 36 = y - 32 = z - 64 is

  • (2, 10, 4)

  • (21, 5/3, 10/3)

  • (5, 7, - 2)

  • (- 3, 3, 6)


B.

(21, 5/3, 10/3)

The point on the linex - 53 = y - 7- 1 = z + 21 = ris (3r + 5, - r + 7, r - 2).This point lies onx + 3- 36 = y - 32 = z - 64   3r + 5 + 3- 36 = - r + 7 - 32 = r - 2 - 64          3r + 8- 36 = - r + 42 = r - 84       - r + 42 = r - 84      - 2r + 8 = r - 8                  3r = 16                    r = 163 Coordinates of the intersection point are16 + 5, - 163 + 7, 163 - 2 i.e., 21, 53, 103


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45.

The distance between the point (1, - 5, - 10) and the point of intersection of the plane x - y + z = 5 and the line x - 23 = y + 14 = z - 212, will be

  • 10

  • 11

  • 12

  • 13


46.

A point is in motion along the curve 12y = x3. The x-coordinate, changes faster than y-coordinate, if

  • x  - 2, 2

  • x  - , - 2  2, 

  • x  - 2, 

  • x  - , 2  2, 


47.

The ratio in which yz-plane divides the line joining (2, 4, 5) and (3, 5, 7) is

  • - 2 : 3

  • 2 : 3

  • 3 : 2

  • - 3 : 2


48.

The y - coordinate of a point P on the line joining A(7, 2,1) and B(10, 5, 7) is 4. Then, x and z - coordinates of the point are

  • x = 9, z = 5

  • x = 3, z = 7

  • x = 2, z = 3

  • None of these


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49.

If point D divides the base BC of a ABC in the ratio n : m, then the value of mBD2 + nCD2 + (m + n)AD2 is

  • mAC2 + nAB2

  • (m + n)(AC2 + AB2)

  • nAC2 + mAB2

  • None of these


50.

The graph of the equation y2 + z2 = 0 in three dimensional space is

  • YZ-plane

  • Z-axis

  • Y-axis

  • X-axis


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