6 cm 6 cm 12 cm In the diagram, O is centre of the rectangular base ABCD of a right pyramid with vertex V. Perpendicular unit vectors i, j, k are parallel to AB, BC and OV respectively. The length of AB, BC and OV are 12 cm, 6 cm and 6 cm respectively. A line 1 has cartesian equation - x-4 - = y +2 = 10 t- z - 2 (i) Find the vector equation of line AV. (ii) If the line I intersects line AV at M, find the position vector of M and the value of t. (iii) Find the acute angle between line AV and the linel. Hence find the perpenUiCuiai distance from A to the line 1. 0. [(i) r =0+1 1 1eR (ii) OM = -2 t = 2 (iii) 60.8°, 2.62]
6 cm 6 cm 12 cm In the diagram, O is centre of the rectangular base ABCD of a right pyramid with vertex V. Perpendicular unit vectors i, j, k are parallel to AB, BC and OV respectively. The length of AB, BC and OV are 12 cm, 6 cm and 6 cm respectively. A line 1 has cartesian equation - x-4 - = y +2 = 10 t- z - 2 (i) Find the vector equation of line AV. (ii) If the line I intersects line AV at M, find the position vector of M and the value of t. (iii) Find the acute angle between line AV and the linel. Hence find the perpenUiCuiai distance from A to the line 1. 0. [(i) r =0+1 1 1eR (ii) OM = -2 t = 2 (iii) 60.8°, 2.62]
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
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![6 cm
6 cm
12 cm
В
In the diagram, O is centre of the rectangular base ABCD of a right pyramid with vertex V.
Perpendicular unit vectors i, j, k are parallel to AB, BC and OV respectively. The length
of AB, BC and OV are 12 cm, 6 cm and 6 cm respectively.
- x-4
t- z
A line 1 has cartesian equation
10
- = y +2 =
- 2
(i)
Find the vector equation of line AV.
(ii)
If the line 1 intersects line AV at M, find the position vector of M and the value of
t.
(iii)
Find the acute angle between line AV and the linel. Hence find the perpenUiCuiai
distance from A to the line 1.
0.
-4
[(i) r =0+1| 1
1 eR (ii) OM:
-2 , t = 2 (iii) 60.8°, 2.62]
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Transcribed Image Text:6 cm
6 cm
12 cm
В
In the diagram, O is centre of the rectangular base ABCD of a right pyramid with vertex V.
Perpendicular unit vectors i, j, k are parallel to AB, BC and OV respectively. The length
of AB, BC and OV are 12 cm, 6 cm and 6 cm respectively.
- x-4
t- z
A line 1 has cartesian equation
10
- = y +2 =
- 2
(i)
Find the vector equation of line AV.
(ii)
If the line 1 intersects line AV at M, find the position vector of M and the value of
t.
(iii)
Find the acute angle between line AV and the linel. Hence find the perpenUiCuiai
distance from A to the line 1.
0.
-4
[(i) r =0+1| 1
1 eR (ii) OM:
-2 , t = 2 (iii) 60.8°, 2.62]
6.
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