NCERT Class XI Mathematics - Introduction to Three Dimensional Geometry - Solutions
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Question : 5
Total: 20
Find the distance between the following pairs of points :
(i) (2, 3, 5) and (4, 3, 1)
(ii) (–3, 7, 2) and (2, 4, –1)
(iii) (–1, 3, –4) and (1, –3, 4)
(iv) (2, –1, 3) and (–2, 1, 3).
(i) (2, 3, 5) and (4, 3, 1)
(ii) (–3, 7, 2) and (2, 4, –1)
(iii) (–1, 3, –4) and (1, –3, 4)
(iv) (2, –1, 3) and (–2, 1, 3).
Solution:
(i) The distance PQ between the points P(2, 3, 5) and Q(4, 3, 1) is
PQ =√ ( 4 − 2 ) 2 + ( 3 − 3 ) 2 + ( 1 − 5 ) 2 √ 4 + 0 + 16 √ 20 2 √ 5
(ii) The distance PQ between the points P(–3, 7, 2) and Q(2, 4, –1) is
PQ =√ ( 2 − ( − 3 ) ) 2 + ( 4 − 7 ) 2 + ( 1 − 12 ) 2
=√ ( 2 + 3 ) 2 + ( 4 − 7 ) 2 + ( − 1 − 2 ) 2 √ 25 + 9 + 9 √ 43
(iii) The distance PQ between the points P(–1, 3, –4) and Q(1, –3, 4) is
PQ =√ ( 1 − ( − 1 ) ) 2 + ( − 3 − 3 ) 2 + ( 4 − ( − 4 ) ) 2
=√ 4 + 36 + 64 √ 104 2 √ 26
(iv) The distance PQ between the points P(2, –1, 3) and Q(–2, 1, 3) is
PQ =
(ii) The distance PQ between the points P(–3, 7, 2) and Q(2, 4, –1) is
PQ =
=
(iii) The distance PQ between the points P(–1, 3, –4) and Q(1, –3, 4) is
PQ =
=
(iv) The distance PQ between the points P(2, –1, 3) and Q(–2, 1, 3) is
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