Vector Algebra questions
907 published questions with worked solutions.
- If a and b are two unit vectors such that 5 a +4 b and a -2 b are perpendicular to each other, then the angle between a and b is
- Let a =2 i + j -2 k and b = i + j . If c is a vector such that a c =| c |, | c - a |=2 2 and the angle between ( a b ) and c is...
- Let L_1: x+2 5 = y-3 2 = z-6 1 and L_2: x-3 4 = y+2 3 = z-3 5 be the given lines. Then the unit vector perpendicular to both L_1...
- If the vectors a= i- j+2 k, b=2 i+4 j+ k and c=p i+ j+q k are mutually orthogonal, then (p,q) is equal to
- If u, v and w are three non-coplanar vectors, then ( u+ v- w ) ( u- v ) ( v- w ) is equal to
- The volume of a parallelopiped with coterminous edges a, b, c is 3 cubic units. The volume (in cubic units) of a tetrahedron with...
- Let a, b and c be three coplanar unit vectors. A unit vector d is perpendicular to them. If ( a b) ( c d)= 3 26 i- 2 13 j+ 6 13 k...
- If a=2 i+ j- k, b= i+3 k, and c is a unit vector, then the maximum value of the scalar triple product [ a b c] is
- If a=4 i+ j+ k, b=2 i+ j+2 k and c=3 i+4 j+5 k, then ( a+ b) ( b+ c)=
- The vector equation of the line whose cartesian equations are x = 2, 2y – 3z + 7 = 0
- The acute angle between the vector 2 i+ j-3 k and the plane containing the vector 2 i+3 j- k and i- j+2 k is
- Let a= i+ j, c= i- j and a vector b be such that a b= c and a b=3 then | b|=
- Let A, B, C, D be the points in the plane with position vectors -2 i- j, 4 i, 3 i+3 j and -3 i+2 j respectively, then is
- If a = i - 2 j + 3 k and b = 2 i + 3 j - k are two vectors, then the angle between the vectors 3 a + 5 b and 5 a + 3 b is
- If a is perpendicular to b and c , | a | = 2, | b | = 3, | c | = 4 and the angle between b and c is 3 , then [ a b c ] =
- If a = 2 i - j + k , b = i + j - 2 k and c = 4 i - 2 j + k , then the unit vector in the direction of 3 a + b - 2 c is
- If a = a_1 i + a_2 j + a_3 k , b = b_1 i + b_2 j + b_3 k , c = c_1 i + c_2 j + c_3 k and [3 a + b 3 b + c 3 c + a ] = vmatrix a i...
- If a = 2 i + 2 j + 3 k , b = - i + 2 j + k and c = 3 i + j are the vectors such that a + b is perpendicular to c , then value of...
- If a , b , c are three vectors such that a 0 and a b = 2 a c , | a | = | c | = 1, | b | = 4 and | b c | = 15 . If b - 2 c = a ,...
- If a, b and c are unit coplanar vectors, then the scalar triple product [2 a- b 2 b- c 2 c- a] has the value
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