A point on a line has coordinates p + 1, p&nb

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 Multiple Choice QuestionsMultiple Choice Questions

21.

If the line x - 41 = y - 21 = z - k2 lies on the plane 2x – 4y + z = 7, then what is the value of k ?

  • 2

  • 3

  • 5

  • 7


22.

A point on the line x - 11 = y - 32 = z + 27 has coordinates

  • (3, 5, 4)

  • (2, 5, 5)

  • ( - 1,  - 1, 5)

  • (2,  - 1, 0)


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23.

A point on a line has coordinates p + 1, p - 3, 2p where p is any real number. What are the direction cosines of the line ?

  • 12, 12, 12

  • 12, 12, 12

  • 12, 12, - 12

  • Cannot be determined due to insufficient data


A.

12, 12, 12

we have co-ordinates of pointp + 1, p - 3, 2p these are the intercepts of respectively.

Then

x = p + 1

x - 1 = p                    ...(i)

y = p - 3

y = 3 = p                  ... (ii)

We can write these three equations as,

z = 2p  z2 = p ...(iii)  

We can write these three equations a,

x - 11 = y +31 = z - 03 = p

We can compare this with standard form 

x - x1a = y - y1b = z - z1c = r

Therefore, direction ratios are a, b, c then 1, 1, 2

Direction cosines are l, m, n

We know

l = aa2 + b2 + c2, m = ba2 + b2 + c2, n = ca2 + b2 + c2l = 112 + 12 + 22, m = 112 + 12 + 22, n = 112 + 12 + 22l = 12, m = 12, n = 12Then direction cosines are 12, 12, 12


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24.

What is the equation of the plane which cuts an intercept 5 units on the z-axis and is parallel to xy-plane ?

  • x + y = 5

  • z = 5

  • z = 0

  • x + y + z = 5


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25.

Into how many compartments do the coordinate planes divide the space ?

  • 2

  • 4

  • 8

  • 16


26.

If a line has direction ratios < a + b, b + c, c + a >, then what is the sum of the square of its direction cosines ?

  • (a + b + c)2

  • 2(a + b + c)

  • 3

  • 1


27.

What is the perpendicular distance from the point (2, 3, 4) to the line x - 01 = y - 00 = z - 00 ?

  • 6 units

  • 5 units

  • 3 units

  • 2


28.

What is the length of the diameter of the sphere whose centre is at (1, 2, 3) and which touches the plane 6x – 3y + 2z – 4 = 0 ?

  • 1 unit

  • 2 units

  • 3 units

  • 4 units


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