NCERT Solutions For Class 12 Maths Chapter 11 Three Dimensional Geometry Exercise 11.2 Question 1 to 17 Answer: Downlaod pdf

Question 1:Show that the three lines with direction cosines 12 3 4 4 12 3 3 4 12 , , ; , ,; , , 13 13 13 13 13 13 13 13 13 are mutually perpendicular.

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Question 2:Show that the line through the points (1, – 1, 2), (3, 4, – 2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).

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Question 3:Show that the line through the points (4, 7, 8), (2, 3, 4) is parallel to the line through the points (– 1, – 2, 1), (1, 2, 5).

Question 4:Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector ˆ ˆ ˆ 32 2 i jk .

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Question 5:Find the equation of the line in vector and in cartesian form that passes through the point with position vector ˆ ˆ 2 4 ij k and is in the direction ˆ ˆ ˆ i jk 2 .

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Question 6:Find the cartesian equation of the line which passes through the point (– 2, 4, – 5) and parallel to the line given by 348 356 xyz .

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Question 7:The cartesian equation of a line is 546 372 xyz . Write its vector form.

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Question 8:Find the vector and the cartesian equations of the lines that passes through the origin and (5

Question 9:Find the vector and the cartesian equations of the line that passes through the points (3, – 2, – 5), (3, – 2, 6).

Question 10:Find the angle between the following pairs of lines: (i) ˆˆ ˆˆ ˆ ˆ r i jk i j k 25 ( 3 2 6) and 7 6 ( 2 2) ˆ ˆ ˆ ˆ ˆ rik i jk (ii) ˆˆ ˆˆ ˆ ˆ r ij k ij k 3 2( 2 ) and ˆˆ ˆ ˆ ˆ ˆ r ij k i j k 2 5 6 ( 3 5 4)

Exercise 11.2 class 12 Math ncert solutions Chapter 11

Question 11:Find the angle between the following pair of lines: (i) 213 2 45 and 2 5 3 18 4 x yz x y z (ii) 523 and 2 2 1 418 xyz x y z

1. Show that the three lines with direction cosine

Question 12:Find the values of π so that the lines 1 7 14 3 32 2 xy z p and 77 56 3 15 xy z p are at right angles.

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Question 13:Show that the lines 5 2 7 51 xyz and 123 xyz are perpendicular to each other.

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Question 14:Find the shortest distance between the lines ˆ ˆ ˆ r i jk (2 ) + ˆ ˆ ˆ ( ) i jk and ˆˆ ˆˆ ˆ ˆ r i jk i j k 2 ( 2 2 )

Question 15:Find the shortest distance between the lines 111 7 61 xyz✁ and 357 1 21 xyz

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Question 16:Find the shortest distance between the lines whose vector equations are ˆ ˆ ˆ ri j k ( 2 3) + ˆ ˆ ˆ ( 3 2) i jk and ˆˆ ˆ ˆ ˆ ˆ r i j k i jk 456 ( 2 3 )

CBSE NCERT Solutions For Class 12 Three Dimensional Geometry

Question 17:Find the shortest distance between the lines whose vector equations are ˆ ˆ ˆ r t (1 ) ( 2) (3 2 ) it j t k and

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