Vector Algebra questions
907 published questions with worked solutions.
- Let ABCD be a quadrilateral. If E and F are the mid points of the diagonals AC and BD respectively and ( AB - BC )+( AD - DC )=k...
- Let S be the set of all values of , for which the shortest distance between the lines x- 0 = y-3 4 = z+6 1 and x+ 3 = y -4 = z-6...
- Let =4 i +3 j +5 k and = i +2 j -4 k . Let _1 be parallel to and _2 be perpendicular to . If = _1 + _2 , then the value of 5 _2...
- If the shortest between the lines x+ 6 2 = y- 6 3 = z- 6 4 and x- 3 = y-2 6 4 = z+2 6 5 is 6, then the square of sum of all...
- Let a = i +2 j + k , b =3 i -5 j - k , a . c =7, 2 b . c +43=0, a c = b c . Then | a . b | is equal to
- Let u = i - j -2 k , v =2 i + j - k , v . w =2 and v w = u + v . Then u . w is equal to
- The shortest distance between the lines x-2 3 = y+1 2 = z-6 2 and x-6 3 = 1-y 2 = z+8 0 is equal to
- Let a =- i - j + k and a . b =1 and a b = i - j . Then a -6 b is equal to
- If the shortest distance between the line joining the points (1, 2, 3) and (2, 3, 4), and the line x-1 2 = y+1 -1 = z-2 0 is ,...
- Let a , b and c be three non zero vectors such that b . c =0 and a ( b c )= b - c 2 . If d be a vector such that b . d = a . b ,...
- The shortest distance between the lines x-1 2 = y+8 -7 = z-4 5 and x-1 2 = y-2 1 = z-6 -3 is
- If a = i +2 k , b = i + j + k , c =7 i -3 j +4 k , r b + b c = 0 and r . a =0. Then r . c is equal to
- The plane 2x – y + z = 4 intersects the line segment joining the points A(a, –2, 4) and B(2, b, –3) at the point C in the ratio 2...
- Let a =4 i +3 j and b =3 i -4 j +5 k . If c is a vector such that c .( a b )+25=0, c .( i + j + k )=4 and projection of c on a is...
- If the vectors a = i + j +4 k , b =-2 i +4 j -2 k and c =2 i +3 j + k are coplanar and the projection of a on the vector b is 54...
- Let a , b and c be three non-zero non-coplanar vectors. Let the position vectors of four points A, B, C and D be a - b + c , a -3...
- Let a and b be two vectors, Let | a | = 1, | b | = 4 and a . b = 2. If c =(2 a b )-3 b , then the value of b . c is
- Let R, a = i +2 j -3 k , b = i - j +2 k If (( a + b ) ( a b )) ( a - b )=8 i -40 j -24 k then | .( a + b ) ( a - b )|^2 is equal...
- If a , b , c are three non-zero vectors and n is a unit vector perpendicular to c such that a = b - n , ( 0) and b . c =12, then...
- The line _1 passes through the point (2, 6, 2) and is perpendicular to the plane 2x + y – 2z = 10. Then the shortest distance...
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