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Crash 2023- Unit test 3 - Entrance oriented questions related on the chapter wise
Mathematics class 11 (041)
University of Kerala
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Crash - 2023
Unit test - 3
Vectors and Three Dimensional Geometry
The vectors which is/are coplanar with vectors k
ˆ
j 2
ˆ
i
ˆ
and k
ˆ
j
ˆ
i 2
ˆ
, are perpendicular to the vector k
ˆ
j
ˆ
i
ˆ
,
is/are
(a) k
ˆ
j
ˆ
(b) iˆ ˆj (c) j
ˆ
i
ˆ
(d) k
ˆ
j
ˆ
If [a b b c c a] = [a b c]
2
, then is equal to
(a) 1 (b) 2 (c) 3 (d) 0
If the vectors AB = k
ˆ
i 4
ˆ
3 and AC = k
ˆ
j 4
ˆ
i 2
ˆ
5 are the
sides of a triangle ABC, then the length of the median through
A is
(a) 18
(b) 72
(c) 33
(d) 45
Let aˆ and b
ˆ
be two unit vectors .If the vectors b
ˆ
c aˆ 2
and b
ˆ
d 5 aˆ 4 are perpendicular to each other, then the
angle between aˆ and b
ˆ
is
(a)
6
(b)
2
(c)
3
(d)
4
If k)
ˆ
i
ˆ
( 3
10
1
a and k)
ˆ j 6
ˆ i 3
ˆ ( 2
7
1
b , then the
value of ( 2 a b){(ab)(a 2 b)}is
(a) -3 (b) 5 (c) 3 (d) -
If the vectors a, b are not perpendicular and c, d are two
vectors satisfying b c = b d and a d 0. Then, the
vector d is equal to
(a) b
a b
a c
c
(b) c
a b
bc
b
(c) b
a b
a c
c
(d) c
a b
b c
b
Let k
ˆ
j
ˆ
a and k
ˆ
j
ˆ
i
ˆ
b . Then, the vector b satisfy-
ing a b + c = 0 and a b 3 , is
(a) k
ˆ
j 2
ˆ
i
ˆ
(b) k
ˆ
j 2
ˆ
i
ˆ
2
(c) k
ˆ
j 2
ˆ
i
ˆ
(d) k
ˆ
j 2
ˆ
i
ˆ
The image of the line
5
z 4
1
y 3
3
x 1
in the plane 2x - y
- z + 3 = 0 is the line
(a)
5
z 2
1
y 5
3
x 3
(b)
5
z 2
1
y 5
3
x 3
(c)
5
z 2
1
y 5
3
x 3
(d)
5
z 2
1
y 5
3
x 3
If the lines
3
z 1
1
y 1
2
x 1
and
4
z
3
y k
2
x 2
are coplanar, then the value of k is
(a) 11/2 (b) - 11/2 (c) 9/2 (d) - 9/
Let Q be the foot of perpendicular from the origin to the plane
4x - 3y + z + 13 = 0 and P be a point (-1,1,-6) on the plane.
Then, length PQ is
(a) 14 (b)
2
19
(c)
2
7
3 (d)
2
3
If the non-zero vectors a,b and c related by a = 8b and c = -7b.
Then, the angle between a and c is
(a) (b) 0 (c)
4
(d)
2
If the vectors k
ˆ
j 2
ˆ
i
ˆ
a , k
ˆ
j
ˆ
i 4
ˆ
b 2 and
k
ˆ
j
ˆ
i
ˆ
c are mutually orthogonal, then , is
equal to
(a) (-3,2) (b) (2,-3) (c) (-2,3) (d) (3,-2)
Let k
ˆ
j
ˆ
i
ˆ
a , k
ˆ
j 2
ˆ
i
ˆ
b and k
ˆ
j
ˆ
i (x 2 )
ˆ
c x . If
the vector c lies in the plane a and b, then x equals
(a) 0 (b) 1 (c) -4 (d) -
1.
2.
3.
4.
5.
6.
7.
11.
12.
13.
14.
15.
16.
8.
9.
10.
17.
18.
19.
Time : 45 minutes
Max Marks : 120
XII
The equation of the plane containing the lines 2x - 5y + z = 3,
x + y + 4z = 5 and parallel to the plane x + 3y + 6z = 1, is
(a) 2x + 6y + 12z = 13 (b) x + 3y + 6z = -
(c) x + 3y + 6z = 7 (d) 2x + 6y + 12z = -
The distance of the point (1,0,2) from the point of intersection
of the line
12
z 2
4
y 1
3
x 2
and the plane x + y + z = 16, is
(a) 2 14 (b) 8 (c)
3 21
(d) 13
The distance of the point (1,-5,9) from the plane x - y + z = 5
measured along a straight line x = y = z , is
(a) 3 5 (b) 10 3 (c) 5 3 (d) 310
If the angle between the line
z 3
2
y 1
x and the
plane x + 2y + 3z = 4 is
14
5
cos
1 , then
is equal to
(a) 3/2 (b) 2/5 (c) 5/3 (d) 2/
The vector k
ˆ
i 4
ˆ
AB 3 and k
ˆ
j 4
ˆ
i 2
ˆ
AC 5 are
sides of the triangle ABC. If the length of the median through
A is 7 5 units, then the value of
is ................
20.
21.
22.
23.
24.
25.
If the lines
4
z 1
3
y 1
2
x 1
and
1
z
2
y k
1
x 3
inter-
sect, then k is equal to
(a) -1 (b) 2/9 (c) 9/2 (d) 0
Distance between two parallel planes 2x + y + 2z = 8 and 4x +
2y + 4z + 5 = 0 is
(a) 3/2 (b) 5/2 (c) 7/2 (d) 9/
The equation of a plane through the line of intersection of
the planes x + 2y = 3, y - 2z + 1 = 0 and perpendicular to
the first plane, is
(a) 2x - y - 10z = 9 (b) 2x - y + 7z = 11
(c) 2x - y + 10z = 11 (d) 2x - y - 9z = 10
An equation of a plane parallel to the plane x - 2y + 2z - 5 = 0
and a unit distance from the origin, is
(a) x - 2y + 2z
3 = 0 (b) x - 2y + 2z + 1 = 0
(c) x - 2y + 2z - 1 = 0 (d) x - 2y + 2z + 5 = 0
Let k
ˆ
j
ˆ
i
ˆ
v 2 and
k
ˆ
i 3
ˆ
w . If uˆ is a unit vector and
p is the maximum value of the scalar triple product [u v w],
then the value of p
2 - 52 is .................
If b
ˆ
aˆ , and cˆ are unit vectors such that b 0 aˆ cˆ
ˆ
aˆ
and the angle between b
ˆ
and cˆ is /3, then the value of
b aˆ cˆ |
ˆ
| aˆ is ................
If the line
2
z k
1
y 2
1
x 4
lies exactly on the plane 2x -
4y + z = 7, then the value of k is .................
If the distance from the line x = 2 + t, y = 1 + t , t
2
1
2
1
z to the plane x + 2y + 6z = 10 is
, then 5 is .....................
If the lines
8
z 11
9
y 17
15
x 4
and
11
z 8
17
y 9
4
x 15
intersect at the point P, then square of the distance of P from the origin
is
, where
- 1390 equals ................
If the shortest distance between the lines
1
z 3
1
y 8
3
x 3
and
4
z 6
2
y 7
3
x 3
is
30
units, then the value of
is
..........................
If the perpendicular distance of the point (6,5,8) from the Y-axis is 5 units, then is equal to ......................
27.
28.
29.
- If b
ˆ
aˆ , and cˆ are unit vectors satisfying b cˆ| |cˆ aˆ| 9
ˆ
b| |
ˆ
| aˆ
2 2 2 , then b 5 cˆ|
ˆ
| 2 aˆ 5 is ...................
26.
Crash 2023- Unit test 3 - Entrance oriented questions related on the chapter wise
Course: Mathematics class 11 (041)
University: University of Kerala
