Vector Algebra questions
907 published questions with worked solutions.
- Let a and b two unit vectors. If the vectors c = a + 2 b and d = 5 a + 4 b are perpendicular to each other, then the angle...
- If the vectors a i+ j+ k, i+b j+ k, i+ j+c k, (a b,c 1) are coplanar, then 1 1-a + 1 1-b + 1 1-c has the value _____.
- If a, b and c are three non-coplanar vectors, then ( a+ b+ c) [( a+ b) ( a+ c) ] equals
- Let a=2 i+ j-2 k and b= i+ j. If c a vector such that a c=| c|, | c- a|=2 2 and the angle between ( a b) and c is 60^0, then the...
- If a= i+ j+ k, a b=1 and a b= j- k, then b is
- If the area of the parallelogram with a and b as two adjacent sides is 15 square units, then the area (in square units) of the...
- If ( a b ) c = -5 a + 4 b and a b = 3, then the value of a ( b c ) is
- If p = i + j + k and q = i - 2 j + k . Then a vector of magnitude 5 3 units perpendicular to the vector q and coplanar with p and...
- If a and b are two unit vectors such that a + 2 b and 5 a - 4 b are perpendicular to each other, then the angle between a and b is
- If a = m b + n c , where a = 4 i + 13 j - 18 k , b = i - 2 j + 3 k , c = 2 i + 3 j - 4 k , then m + n =
- If the volume of tetrahedron, whose vertices are with position vectors i - 6 j + 10 k , - i - 3 j + 7 k , 5 i - j + k and 7 i - 4...
- The value of , so that the volume of parallelepiped formed by i + j + k , j + k and i + k becomes minimum, is
- If a=2 i+3 j+2 k, b=2 i+ j- k, and c= i+3 j are such that ( a+ b) is perpendicular to c, then the value of is
- The vector projection of AB on CD , where A (2,-3,0), B (1,-4,-2), C (4,6,8) and D (7,0,10), is
- The vectors a=2 i+ j-2 k, b= i+ j. If c is a vector such that a c=| c| and | c- a|=2 2, angle between a b and c is 4, then |( a...
- If a= i+2 j+ k, b= i- j+ k, c= i+ j- k, then a vector in the plane of a and b, whose projection on c is 1 3 , is
- Let a, b, c be three non-zero vectors, such that no two of them are collinear and ( a b) c= 13| b|| c| a. If is angle between the...
- Let P, Q, R and S be the points on the plane with position vectors -2 i- j, 4 i, 3 i+3 j and -3 i+2 j respectively. Then the...
- If the points P, Q and R are with the position vectors i-2 j+3 k, -2 i+3 j+2 k and -8 i+13 j respectively, then these points are
- One side and one diagonal of a parallelogram are represented by 3 i+ j- k and 2 i+ j-2 k respectively, then the area of...
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