The vertices of a AABC are A (2, 0, 2), B (- 1, 1, 1) and C(1,-2,4). The points D and E divide the sides AB and AC in the ratio 1: 2grespectively. Another point F is taken in space such that perpendicular drawn from F on AABC meet the A at the point of intersection of line segment CD and BE at P. If distance of F from plane of AABC is 2 units, then

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
icon
Related questions
Question
100%
The vertices of a A4BC are A (2, 0, 2), B (- 1, 1, 1) and
C(1,-2,4). The points D and E divide the sides AB and AC
in the ratio 1: 2jrespectively. Another point F is taken in
space such that perpendicular drawn from F on AABC meet
the A at the point of intersection of line segment CD and BE
at P. If distance of F from plane of AABC is 2 units, then
→and 2:1
5.
The position vector of P is
(a) i-j+3R
(b) i-)
(c) 21-j-3k
(d) i+j+3k
6.
The volume of tetrahedron ABCF is
(a) cubic units
(b) cubic units
(c)
cubic units
(d) 7cubic units
7.
The vector PF is
(a) î+3
(b) +k
(c) 7i+ 7k
8.
The equation of line AF is
(a) = (i+k)+2(î+ĵ
(b) = (2i+2k)+2(-i+2Â)
(c) 7=(2i+2j)+2(-î+ĵ+Â)
(d) none of these
Transcribed Image Text:The vertices of a A4BC are A (2, 0, 2), B (- 1, 1, 1) and C(1,-2,4). The points D and E divide the sides AB and AC in the ratio 1: 2jrespectively. Another point F is taken in space such that perpendicular drawn from F on AABC meet the A at the point of intersection of line segment CD and BE at P. If distance of F from plane of AABC is 2 units, then →and 2:1 5. The position vector of P is (a) i-j+3R (b) i-) (c) 21-j-3k (d) i+j+3k 6. The volume of tetrahedron ABCF is (a) cubic units (b) cubic units (c) cubic units (d) 7cubic units 7. The vector PF is (a) î+3 (b) +k (c) 7i+ 7k 8. The equation of line AF is (a) = (i+k)+2(î+ĵ (b) = (2i+2k)+2(-i+2Â) (c) 7=(2i+2j)+2(-î+ĵ+Â) (d) none of these
Expert Solution
steps

Step by step

Solved in 6 steps

Blurred answer
Knowledge Booster
Cartesian Coordinates
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning