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Vector Algebra Questions and Answers pt3
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Vector Algebra Questions and Answers pt3
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JEE ADVANCED - VOL - I VECTOR ALGEBRALEVEL-VI 11
(A) n ,nZ (B) 2n ,nZ
6 6
SINGLE ANSWER QUESTIONS
11
(C) 2n , n Z (D) 2n ,nZ
^ ^ ^ 6 6
1. The unit vector c if i j k bisects the
5. If b is vector whose initial point divides the
^ ^
^
angle between vectors c and 3 i 4 j is ^
join of 5 i and 5 j in the ratio k:1 and whose
1 ^ ^ ^
(A) 11 i 10 j 2 k terminal point is the origin and b 37 ,
15
then k lies in the interval
1 ^ ^ ^
(B) 11i 10 j 2 k 1 1
15 (A) 6, (B) , 6 ,
6 6
1 ^ ^ ^
(C) 11 i 10 j 2 k 1
15 (C) 0, 6 (D) 6,
5
1 ^ ^ ^
(D) 11 i 10 j 2 k 6. Let x 2 3 y 2 3 be the equation of an ellipse
15
2. A man travelling east at 8km/h finds that the in the xy-plane. A and B are two points whose
wind seems to blow directly from the north. ^ ^
On doubling the speed, he finds that it position vectors are 3 i and 3 i 2 k
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appears to come from the north-east. The then the position vector of a point P on the
velocity of the wind is ellipse such that APB / 4 is
(A) 450 , v 8 2 (B) 450 , v 8 2
(C) 900 , v 4 2 (D) 600 , v 8 2
3. ABCD is a parallelogram . If L and M be
the middle points of BC and CD,
respectively express AL and AM in terms ^ ^ ^
(A) j (B) i j
of AB and AD . If AL AM K . AC then
the value of K is ^
(A) 1/2 (B) 3/2 (C) 2 (D) 1 (C) i (D) k
4. If the vectors a and b are linearly ^ ^ ^ ^ ^ ^
7. If vectors a 3 i j 2 k , b i 3 j 4 k
independent satisfying
^ ^ ^
3 tan 1 a 3 sec 2 b 0 , then and c 4 i 2 j 6 k constitute the sides of
the most general values of are ABC , then the length of the median
bisecting the vector c
160 Narayana Junior Colleges
,VECTOR ALGEBRA JEE ADVANCED - VOL - I
A) Equilateral triangle B) Isosceles triangle
14
(A) 2 (B) (C) 74 (D) 6 C) Scalene triangle D) Straight line
2 13. Any plane cuts the sides AB, BC, CD, DA
8. Let AC be an arc of a circle, subtending a of a quadrilateral in P, Q, R, S respectively,
right angle at the centre O. The point B
divides the arc AC in the ratio 1:2 . If AP BQ CR
and if 1 , 2 , 3 ,
PB QC RD
OA a and OB b , then calculate OC in
DS
terms of a and b 4 . Then 1234
SA
A) 1 B) 2 C) 3 D) 4
14. Points X and Y are taken on the sides QR
and RS respectively of a parallelogram
PQRS. So that QX 4 XR and RY 4YS the
PZ
line XY cuts the line PR at Z then
(A) 2b 3 a (B) 2b 3 a ZR
1 21 21 16
(C) 2b 3 a (D) 3b 2 a
A) B) C) D)
9. ABC is a triangle and O any point in the same 4 5 4 3
plane. AO, BO and CO meet the sides BC, 15. Let OABCD is a pentagon in which the side
CA and AB respectively at points D, E and OA and CB are parallel and the sides OD
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OD OE OF and AB are parallel and OA : CB 2 :1 and
F then
AD BE CF OD : AB 1: 3 . If the diagonal OC and AD
(A) 1 (B) 1/2 (C) 1/3 (D) 2 OX
10. In triangle ABC, A 300 , H is the meet at X then
XC
orthocenter and D is the mid-point of BC.
Segment HD is produced to T such that 1 1 2 2
HD=DT. The length AT is equal to A) B) C) D)
3 5 3 5
4 1 16. Let a i j , b j k . If ‘m’ be slope of
A) 2BC B) 3BC C) BC D) BC
3 3
11. The value of so that the points P, Q, R tangent to the curve y f x at x 1
and S on the sides OA, OB, OC and AB of a
regular tetrahedron OABC are coplanar 3x 4 4
where f x 2 x R
OP 1 OQ 1 OR 1 3x 4 3
when , , and
OA 3 OB 2 OC 3 then the vector of magnitude “m” along the
OS
then bisector of angle between a and b is
AB
1 3 3 2
A)
2
B) 1 A)
2
i 2 j k B) 3
i j 2k
C) 0 D) for no value of
12. In triangle ABC, AD and AD' are the 2 i jk
bisectors of the angle A meeting BC in D
C)
3 3
i 2 j k D) 2
and D ' respectively. A ' is the mid point of 17. If the resultant of two forces is equal in
DD ' ; B ' and C ' are the points on CA and magnitude to one of the components and
perpendicular to it in direction , find the other
AB similarly obtained then A ', B ', C ' forms
component using the vector method
Narayana Junior Colleges 161
, JEE ADVANCED - VOL - I VECTOR ALGEBRA
a b .c
A) 2b a 2 2 c
c
a b .c
B) b a 2 c
c
(A) 1350 (B) 1200 (C) 900 (D) 450
a b .c
C) b a c 2 a D) None
18. If the vector tan , 1, 2 sin 2 and
b
22. The lar distance from A 1, 4, 2 from the
segment BC where B 2,1, 2 ,
3
c tan , tan , C 0, 5,1
are orthogonal
sin
2 3 26 26 3
A) B) C) D) 26
7 7 7
and a vector a 1,3,sin 2 makes an obtuse
angle with the z-axis then the value of is 23. If a, b, c are unit vectors such that
1
A) 4n 1 tan 2
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a 2b 3c 3 2 2 , angle between a
B) 4n 2 tan 1 2
and b is , angle between a and c is
C) 4n 1 tan 1 2
and angle between b and c varies in
D) 4n 2 tan 1 2
19. Image of the point P with position vector 2
2 , 3 then the greatest value of
7iˆ ˆj 2kˆ in the line whose vector equation
4 cos 6 cos
is r 9iˆ 5 ˆj 5kˆ iˆ 3 ˆj 5kˆ has the
position vector A) 2 2 5 B) 2 2 5
A) 9iˆ 5 ˆj 2kˆ B) 9iˆ 5 ˆj 2kˆ C) 2 2 5 D) 42
C) 9i 5 ˆj 2kˆ D) 9iˆ 5 ˆj 2kˆ 24. Let P, Q, R and S be the points on the plane
20. Foot of the perpendicular from the point with position vectors –2 ˆi ˆj, 4i,3i
ˆ ˆ 3jˆ and
P a to the line r b tc 3iˆ 2ˆj respectively. The quadrilateral
PQRS must be a [IIT JEE 2010]
a b .c a.c (A) parallelogram, which is neither a rhombus
A) b 2 c B) b 2 c nor a rectangle
c c
(B) square
(C) rectangle, but not a square
b c .c (D) rhombus, but not a square
C) a c 2 c D) None 25. Two adjacent sides of a parallelogram ABCD
are given by AB 2iˆ 10ˆj 11kˆ and
21. The reflection of the point P a with
AD ˆi 2ˆj 2kˆ . The side AD is rotated by
respect to the line r b tc
an acute angle a in the plane of the
162 Narayana Junior Colleges
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