Find equation of plane
(i) Which passes through (0, 1, 0), (0, 0, 1), (1, 2, 3)
(ii) Which passes through (0, 1, 0) and contains two vectors 
& 
.
(iii) Whose normal is 
& which passes through (1, 2, 1).
(iv) Which makes equal intercepts on co-ordinate axis and passes through (1, 2, 3)
Text Solution
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(i)4x – y – z + 1 = 0 (ii)x + 2y + 3z – 2 = 0
(iii)x + y + z – 4 = 0
(iv) x + y + z – 6 = 0
Sol. (i) 
= 0 ⇒ x(–3 – 1) – (y – 1)(0 – 1) + z(1) = 0
–4x + y – 1 + z = 0 ⇒ 4x – y – z + 1 = 0
(ii) 
= 0 ⇒ x(–1) – (y – 1)(2) + z(–1 – 2) = 0
–x – 2y + 2 – 3z = 0 ⇒ x + 2y + 3z – 2 = 0
(iii) x + y + z = 1 + 2 + 1 ⇒ x + y + z – 4 = 0
(iv) x + y + z = 1 + 2 + 3 ⇒ x + y + z – 6 = 0
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