Vector Algebra questions
907 published questions with worked solutions.
- a , b , c are noncoplanar vectors and p , q , r are defined as p = b c [ b c a ] , q = c a [ c a b ] , r = a b [ a b c ] . ( a +...
- If a , b , c are three noncoplanar vectors represented by concurrent edges of a parallelepiped of volume 4 then ( a + b ) ( b c )...
- If a , b , c are three noncoplanar nonzero vectors then ( a a ) , b c + ( a b ) , c a + ( a c ) , a b is equal to
- Let r be a vector perpendicular to a + b + c , where [ a b c ] = 2. If r = l( b c ) + m( c a ) + n( a b ) then l + m + n is
- If a , b are nonzero and noncollinear vectors then [ a b i ] , i + [ a b j ] , j + [ a b k ] , k is equal to
- The three concurrent edges of a parallelepiped represent the vectors a , b , c such that [ a b c ] = . Then the volume of the...
- i ( a i ) + j ( a j ) + k ( a k ) is equal to
- Let a , b and c be three vectors having magnitudes 1, 1 and 2 respectively. If a ( a c ) + b = 0 , the acute angle between a and...
- If b is a unit vector then ( a b ) , b + b ( a b ) is equal to
- Let a , b , c be three unit vectors such that a ( b c ) = b + c 2 and the angles between a , c and a , b be and respectively then
- Let p , q , r be three mutually perpendicular vectors of the same magnitude. If a vector x satisfies the equation p ( x - q ) p +...
- If and represent dot product and cross product respectively then which of the following is meaningless?
- ( a i )^2 + ( a j )^2 + ( a k )^2 is equal to
- If a b c then ( a b ) ( a c ) is equal to
- If a , b , c are noncoplanar nonzero vectors then ( a b ) ( a c ) + ( b c ) ( b a ) + ( c a ) ( c b ) is equal to
- If a , b , c are three noncoplanar nonzero vectors and r is any vector in space then ( a b ) ( r c ) + ( b c ) ( r a ) + ( c a )...
- Let a , b , c be three unit vectors of which b and c are nonparallel. Let the angle between a and b be and that between a and c...
- 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 30^ then |( a...
- Let a and b be two noncollinear unit vectors. If u= a-( a b) b and v= a b then | v| is
- If a, b, c be three vectors such that [ a b c]=4 then [ a b b c c a] is equal to
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