3. Name the octants in which the following points lie:
(1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (– 4, 2, –5), (– 4, 2, 5), (–3, –1, 6) (– 2, – 4, –7).
3. Name the octants in which the following points lie:
(1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (– 4, 2, –5), (– 4, 2, 5), (–3, –1, 6) (– 2, – 4, –7).
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1 Answer
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3.
Octants
I
II
III
IV
V
VI
VII
VIII
coordinates
x
+
–
+
–
+
y
+
–
+
–
–
z
+
–
–
(1, 2, 3) lies in octant I.
(4, –2, 3) lies in octant IV.
(4, –2, –5) lies in octant VIII.
(4, 2, –5) lies in octant V.
(–4, 2, –5) lies in octant VI.
(–4, 2, 5) lies in octant II.
(–3, –1, 6) lies in octant III.
(–2, –4, –7) lies in octant VII.
Similar Questions for you
Direction ratio of line (1, -1, -6)
Equation of line (x−3)/1 = (y+4)/-1 = (z+5)/-6 =k
x=k+3, y=−k−4, z=−6k−5
Solving with plane k=−2
⇒x=1, y=−2, z=7
⇒Distance=√ (3−1)²+6²+3²=√49=7
Any point on line (1)
x=α+k
y=1+2k
z=1+3k
Any point on line (2)
x=4+Kβ
y=6+3K
Z=7+3K?
⇒1+2k=6+3K, as the intersect
∴1+3k=7+3K?
⇒K=1, K? =−1
x=α+1; x=4−β
⇒y=3; y=3
z=4; z=4
Equation of plane
x+2y−z=8
⇒α+1+6−4=8 . (i)
and 4−β+6−4=8 . (ii)
Adding (i) and (ii)
α+5−β+12−8=16
α−β+17=24
⇒α−β=7
f (x)= {sinx, 0≤x<π/2; 1, π/2≤x≤π 2+cosx, x>π}
f' (x)= {cosx, 0
f' (π/2? ) = 0
f' (π/2? ) = 0
f' (π? ) = 0
f' (π? ) = 0
⇒ f (x) is differentiable in (0, ∞)
Let direction ratio of the normal to the required plane are l, m, n
Equation of required plane
11 (x – 1) + 1 (y – 2) + 17 (z + 3) = 0
Any point on line
5r + 12 = 17
r = 1
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