Vector Algebra questions
907 published questions with worked solutions.
- If a , b , c are three vectors such that a ( b + c ), b ( c + a ), and c ( a + b ) and | a |=1,| b |=2,| c |=3, then | a + b + c...
- Let r (3 i -2 j +7 k )=32 is the equation of a plane and the line having direction ratios (5, b, 3) is parallel to the plane,...
- The shortest distance between the lines r =(4 i - j )+ ( i +2 j -3 k ) and r =( i - j +2 k )+ ( i +4 j -5 k ) is...
- If ABC is a right-angled triangle in which BC is the longest side and position vector of B and C are respectively 3 i -2 j + k...
- The sum of all real values of for which the vectors a = i + j + k , b = i + j +2 k , c =2 i +3 j + k are coplanar is...
- The value of x so that the volume of the parallelopiped formed by the vectors i +x j + k , j +x k and x i + k is minimum, is
- If | a |=3,| b |=4,| c |=5 such that each vector is perpendicular to the sum of the other two, then | a + b + c | is equal to
- If A( a ),B( b ) and C( c ) are vertices of . Point D divides segment BC internally in the ratio 2 : 1. Point E divides segment...
- If p is the shortest distance between the lines x+1 7 = y+1 -6 =z+1 and r =(3 i +5 j +7 k )+ ( i -2 j + k ) then [p], is…, (where...
- If a = i + j , b = 2 i - k then the point of intersection of the lines r a = b a and r b = a b is
- If the projection of a on b + c is twice the projection of b + c on a also if | b | = 2 2 , | c | = 4 and the angle between b and...
- If a and b are unit vectors and is the angle between them, then 2 =
- If a = 1 10 (3 i + k ) and b = 1 7 (2 i +3 j -6 k ) then the value of (2 a - b ) [( a b ) ( a 2 b ) ]=
- If the shortest distance between the lines x-k 2 = y-4 3 = z-3 4 and x-2 4 = y-4 6 = z-7 8 is 13 29 , then k =
- If a , b , c , d are unit vectors such that a b = 1 2 , c d = 1 2 and the angle between a b and c d is 6 , then the value of |[ a...
- If a = 4 i + 3 j + k , b = i - 2 j + 2 k then ( a ( a ( a b ) ) ) =
- If a and b are unit vectors and is the angle between them, then a + b is a unit vector when is
- The magnitude of a vector which is orthogonal to the vector i + j + k and is coplanar with the vectors i + j + 2 k and i + 2 j +...
- Given the following expression A) ( a b ) c B) a ( b c ) C) a ( b c ) D) | a |( b c ) E) ( a b ) ( b c ) Then which of the...
- The volume of the parallelopiped whose coterminous edges are 2 i + j - k , 3 i - j - k , j +3 k is
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