Vector Algebra questions
907 published questions with worked solutions.
- If the vector c lies in the place of a and b, where a= i- j+2 k, b= i+ j+ k and c=x i-(2-x) j- k, then the value of x is
- The foot of the perpendicular drawn from origin to a plane is M (2,1,-2), then vector equation of the plane is
- If a= i- k, b=x i+ j+(1-x) k, and c=y i+x j+(1+x-y) k, then a ( b c) depends on
- If a and c are unit vectors inclined at 3 with each other and ( a b c ) ( a c )=5, then the value of 5 [ a b c ]=
- If | a|=2, | b|=3 and a, b are mutually perpendicular vectors, then the area of the triangle whose vertices are 0, a + 2b, a - 2b...
- Let A, B, C be vectors of lengths 3 units, 4 units, 5 units respectively. Let A be perpendicular to B+ C, B be perpendicular to...
- Let a, b and c be three non-zero vectors such that no two of them are collinear and ( a b) c= 13| b|| c| a. If is the angle...
- If a, b, c are the three unit vectors such that | a+ b+ c|=1 and b is perpendicular to c. If a makes angles , with b and c...
- If a = i + j + k, b = - i + 2 j - 2 k and c = 2 i - j + 2 k, then ( a - b) [( a b) ( a c) ] is
- Let n be a vector of magnitudes 3 3 such that it makes equal acute angles with the co-ordinate axes. Then the vector equation of...
- If a = i + j, b = 2 i - k, then point of intersection of the lines r a = b a and r b = a b is
- The parallelopiped is determined by vectors a =-2 i +5 j +3 k , b = i +3 j -2 k , c =-3 i + j +4 k . The altitude of...
- Let a , b , c be the unit vectors such that a is perpendicular to b and the angle between b and c is 120^ . If a + c is...
- The vector equation of the plane passing through the point A(-2, 7, 5) and parallel to the vectors 4 i - j +3 k and i + j + k is...
- If D and E are the midpoints of the sides BA and BC of triangle ABC, then AE + DC =
- If 7 j + 10 k , - i + 6 j + 6 k and -4 i + 9 j + 6 k are the position vectors of the vertices A, B and C respectively of ABC....
- The vector a + 3 b is perpendicular to 7 a - 5 b and the vector a - 4 b is perpendicular to 7 a - 2 b . Then the angle between a...
- If a = i + j + k , b =4 i +3 j +4 k and c = i + j + k are linearly dependent vectors and | c |= 3 , then the values of and are...
- Let a =2 i + j -2 k , b = i + j and c be a vector such that | c - a |=4, |( a c ) c |=3, and the angle between c and a b is 6 ,...
- If a =2 i +3 j +2 k , b =2 i + j - k and c =3 i - j are such that a + b is perpendicular to c , then the value of is
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