..... Miscellaneous Exercise ..... Show that ...

NCERT Class XII Mathematics Chapter - - Solutions

Question : 60 of 78

Marks: +1, -0

..... Miscellaneous Exercise .....

Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, –1), (4, 3, –1).

Solution:

The direction ratios of the line joining, O(0, 0, 0) and A(2, 1, 1) are < 2 – 0, 1 – 0, 1– 0 > i.e. < 2, 1, 1 >

The direction ratios of the line joining B(3, 5, – 1) and C(4, 3, –1) are < 4 – 3, 3 – 5, – 1 + 1 > i.e. < 1, – 2, 0 >

Now, (2) (1) + (1) (–2) + (1) (0) = 2 – 2 + 0 = 0

Hence OA is perpendicular to BC.

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