Vector Algebra Practice Questions - DPP for JEE

 Page 2


therefore any vector  can be expressed in terms of 
.
Let ....(1)
Taking dot product with  in eq. (1),
we get, 
Taking dot product with  in eq. (1), we get
Taking dot product with  in eq. (1), we get
 
4. (d) …(1)
 if 
for which  if  lies in the second quadrant
? 
General value is 
5. (a) Let O be the origin and the bisector of  meets BC at D. Then 
 and position vector of D is given by
Page 3


therefore any vector  can be expressed in terms of 
.
Let ....(1)
Taking dot product with  in eq. (1),
we get, 
Taking dot product with  in eq. (1), we get
Taking dot product with  in eq. (1), we get
 
4. (d) …(1)
 if 
for which  if  lies in the second quadrant
? 
General value is 
5. (a) Let O be the origin and the bisector of  meets BC at D. Then 
 and position vector of D is given by
  
 
? p.v. of 
 
Page 4


therefore any vector  can be expressed in terms of 
.
Let ....(1)
Taking dot product with  in eq. (1),
we get, 
Taking dot product with  in eq. (1), we get
Taking dot product with  in eq. (1), we get
 
4. (d) …(1)
 if 
for which  if  lies in the second quadrant
? 
General value is 
5. (a) Let O be the origin and the bisector of  meets BC at D. Then 
 and position vector of D is given by
  
 
? p.v. of 
 
6. (c) Q  = 
=  = 
[ Q  is parallel to ]
=  = 
7. (d)  lies in the plane of   and 
?
? a = 1, 2 = 1+ ?, ß = ? ? a = 1, ß = 1
8. (b) Let 
Let  be unit vectors along  respectively. Clearly 
are mutually perpendicular vecotrs, so any vector  can be
weitten as .
?
Similarly, 
and 
According to the given condition
Page 5


therefore any vector  can be expressed in terms of 
.
Let ....(1)
Taking dot product with  in eq. (1),
we get, 
Taking dot product with  in eq. (1), we get
Taking dot product with  in eq. (1), we get
 
4. (d) …(1)
 if 
for which  if  lies in the second quadrant
? 
General value is 
5. (a) Let O be the origin and the bisector of  meets BC at D. Then 
 and position vector of D is given by
  
 
? p.v. of 
 
6. (c) Q  = 
=  = 
[ Q  is parallel to ]
=  = 
7. (d)  lies in the plane of   and 
?
? a = 1, 2 = 1+ ?, ß = ? ? a = 1, ß = 1
8. (b) Let 
Let  be unit vectors along  respectively. Clearly 
are mutually perpendicular vecotrs, so any vector  can be
weitten as .
?
Similarly, 
and 
According to the given condition
9. (c) are unit vectors and equally inclined to
each other at an acute angle ?.
?  ABC is an equilateral triangle
and 
= 
?  Area of ? ABC
= 
If G is the centroid of the ? ABC, then
OG = 
= 
= 
?  = Volume of parallelopiped
= OG × 2 ar (? ABC)
= 
= 
10. (d) Let A be the first term and x the common ratio of G.P.