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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 7 of 78
Marks: +1, -0
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).
Solution:  
Let the given points be A(1, –1, 2), B(3, 4, –2), C(0, 3, 2) and D(3, 5, 6).
The direction ratios of AB are < 3 – 1, 4 + 1, –2 –2 > or <2, 5, – 4> and the direction ratios of CD are < 3 – 0, 5 – 3, 6 – 2 > or <3, 2, 4 >
Two lines with direction ratios a1,b1,c1a_1, b_1, c_1 and a2,b2,c2a_2, b_2, c_2 are perpendicular if
a1a2+b1b2+c1c2=0a_1a_2 + b_1b_2 + c_1c_2 = 0
⇒ 2 × 3 + 5 × 2 + (–4) × 4 = 6 + 10 – 16 = 0
∴ AB and CD are perpendicular.
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