Vector Algebra questions
907 published questions with worked solutions.
- If [ a b b c c a]= [ a b c]^2, then is equal to
- 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
- Let a = i + j + k , b = 2 i + 4 j + 4 k , c = i + j + k . If a is parallel to b and b is perpendicular to c then - = ....
- If | a b | = | a b |, a b < 0 and is the angle between a and b , then the value of + .....
- The value of b such that the scalar product of the vector i + j + k with the unit vector parallel to the sum of the vectors 2 i +...
- Let a and b be linearly independent vectors such that | a | = 3 , | b | = 3 and | a - b | = 4 If a (2 i + 2 j - k ) = (2 i + 2 j...
- Let a=2 i-3 j+ k, b=3 i+2 j+2 k, c=4 i-3 j+ k, then the vectors a, b, c are
- If the lines r= i+ j- k+ (q i-2 j+ k) and r=p i-3 j+2 k+ ( i-2 j+2 k) intersect each other and q i-2 j+ k is collinear to 4 i-4...
- If a b= and a b= c then a=
- The value of (0, 2 ) for which vectors a=( ) i+( ) j and b= i- 3 j+2 k are perpendicular is
- If the volume of the tetrahedron whose coterminous edges are given by the vectors a=-2 i+3 j-3 k, b=4 i+5 j+( -10) k, c=6 i+2 j-3...
- The equation of the plane passing through the points having position vectors ( a+ b),( b+ c) and ( a+ c) is ...
- A vector which is orthogonal to the vector a = i +2 j +3 k and coplanar with the vectors b =3 i +2 j and c =2 i + j +3 k is
- Let a , b , c be three vectors of equal magnitude such that the angle between a and b is , b and c is , c and a is Then the...
- Let u , v , w be three vectors such that | u |=1,| v |=2,| w |=3. If the projection of v along u is equal to the projection of w...
- If a , b , c are three vectors such that | a | = 3, | b | = 5, | c | = 7 then | a - b |^2 + | b - c |^2 + | c - a |^2 does not...
- If [2 p-3 r q s]+[3 p+2 q r s]=m[ p r s]+n[ q r s]+t[ p q s], then the values of m, n, t respectively are ....
- The volume of the tetrahedron whose co-terminus edges are a, b, c is 12 cubic units. If the scalar projection of a on b c is 4,...
- Let O(0, 0), A(-1, 2) and B(1, 3) be the vertices of . The bisector of angle O intersects side AB at point D. The value of OD AB...
- The maximum volume of a parallelopiped (in cubic units) with vectors (2a , i + k ), (a , j -a , k ), and (3 i +a , j ), where a...
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