Vector Algebra questions
907 published questions with worked solutions.
- If the vectors a = i - j + 2 k, b = 2 i + 4 j + k and c = i + j + k are mutually orthogonal, then ( , ) =
- If a = 1 10 (3 i + k) and b = 17(2 i + 3 j - 6 k), then the value of (2 a - b) [( a b) ( a + 2 b)] is
- The vector a and b are not perpendicular and c and d are two vectors satisfying: b c = b d and a d = 0. Then the vector d is...
- The unit vector which is orthogonal to the vector 5 i +2 j +6 k and is coplanar with the vectors 2 i + j + k and i - j + k is
- Let A =2 i + k , B = i + j + k and C =4 i -3 j +7 k . If a vector R satisfies R B = C B and R A =0, then R is given by
- Distance between the parallel lines x 3 = y-1 -2 = z 1 and x+4 3 = y-3 -2 = z+2 1
- If C is a given non-zero scalar and A and B are given non-zero vectors such that A is perpendicular to B . If vector X is such...
- If a = i +2 j +3 k and b = i ( a i )+ j ( a j )+ k ( a k ) then | b | is
- The equation of the line, through A(1,2,3) and perpendicular to the vector 2 i + j - k and i +3 j +2 k , is
- The vector equation of a line whose Cartesian equations are y = 2, 4x – 3z + 5 = 0 is
- The volume of parallelepiped formed by vectors i +m j + k , j +m k and m i + k becomes minimum when m is
- If the vectors a = i - j +2 k , 2 i +4 j + k and c =m i + j +n k are mutually perpendicular then (m, n) is
- If a =(2 i +2 j +3 k ), b =(- i +2 j + k ) and c =(3 i + j ) such that ( a + b ) is perpendicular to c , then the value of is
- If x_0 is the point of local minima of f(x)= a ( b c ) where a =x i -2 j +3 k , b =2 i +x j - k , c =7 i -2 j +x k , then value...
- a , b , and c are three unit vectors such that a ( b c )= 3 2 ( b + c ). If b is not parallel to c , then the angle between a and...
- For all real x, the vectors Cx i -6 j -3 k and x i +2 j -2Cx k make an obtuse angle with each other then the value of C can be in
- The vectors a and b are not perpendicular and c and d are two vectors satisfying b c = b d and a d = 0, then the vector d is...
- If a = 1 10 (4 i - 3 j + k ), b = 1 5 ( i + 2 j + 2 k ), then the value of (2 a - b ) ( a b ) ( a + 2 b ) is
- If a = a_1 i + a_2 j + a_3 k , b = b_1 i + b_2 j + b_3 k and c = c_1 i + c_2 j + c_3 k are non-zero non-coplanar vectors and m is...
- Let L_1: x+1 3 = y+2 2 = z+1 1 and L_2: x-2 2 = y+2 1 = z-3 3 be the given lines. Then the unit vector perpendicular to L_1 and...
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