Vector Algebra questions
907 published questions with worked solutions.
- The number of integral values of p for which the vector (p+1) i-3 j+p k, p i+(p+1) j-3 k and -3 i+p j+(p+1) k are linearly...
- If p=2 i+ k, q= i+ j+ k, r=4 i-3 j+7 k and a vector m is such that m q= r q, m p=0, then m= ..
- If the point (1, , ) lies on the line of the shortest distance between the lines x+2 -3 = y-2 4 = z-5 2 and x+2 -1 = x+2 -1 = y+6...
- If the area of parallelogram, whose diagonals are i- j+2 k and 2 i+3 j+ k is 93 2 sq. unit, then =
- If the lengths of three vectors a, b and c are 5, 12, 13 units respectively, and each one is perpendicular to the sum of the...
- If the vectors m i +m j +n k , i + k , n i +n j +p k lie in a plane then...
- The area of a parallelogram whose diagonals are the vectors 2 a - b and 4 a -5 b , where a and b are unit vectors forming an...
- If a , b , c are three unit vectors such that | a + b |^ 2 +| a + c |^ 2 =8, then | a +3 b |^ 2 +| a +3 c |^ 2 =
- a = i - j , b = j - k , c = k - i then a unit vector d such that a d =0=[ b c d ] is
- Let a= i+ j, b=2 i- k, c=3 i- j+ k, then vector p satisfying p a=0 and p b= c b is
- Let a, b, c be three vectors such that a+ b+ c= 0, | a|=3, | b|=4, | c|=5, then a b+ b c+ c a=
- Let a, b, c, d are vectors such that a b=2 i+3 j- k and c d=3 i+2 j- k and if vmatrix a c& b c a d& b d vmatrix =0, then =
- The area of the rectangle having vertices P, Q R, S with position vectors - i+ j+ k, i+ j+ k, i- j+ k, - i- j+ k respectively is
- Let a=2 i+ j+ k, b= i+2 j- k, and vector c be coplanar. If c is perpendicular to a, then c is
- If is an obtuse angle between vector a and b such that | a | = 5, | b | = 3 and | a b | = 5 5 then a b =
- The Cartesian equation of the plane r = (2 i - 3 j ) + ( i + 2 j - k ) + (2 i + 3 j + k ) is
- If the vectors a = c( _7 x) i + 2 j + 3 k and b = ( _7 x) i + 3c( _7 x) j - 4 k make obtuse angle for any x > 0, then c belongs to
- The altitude through vertex A of ABC with position vectors of points A, B, C as a , b , c respectively is
- If b and c are unit vectors and | a | = 7, a ( b c ) + b ( c a ) = 1 2 a , then angle between the vectors a and c and angle...
- Let a = i + j - k and c = 5 i - 3 j + 2 k and if b c = a then | b | =
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