Vector Algebra questions
907 published questions with worked solutions.
- If a and b are unit vectors and c= b-( a c), then minimum value of [ a b c] is
- A line L_1 passes through the point, whose p.v. (position vector) 3 i, is parallel to the vector - i+ j+ k. Another line L_2...
- If a=2 i+3 j-4 k and b= i- j- k, then the projection of b in the direction of a is
- 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...
- If | a | = 2, | b | = 3, | c | = 5 and each of the angles between the vectors a and b , b and c , c and a is 60^0, then the value...
- Let a = i + 2 j - k and b = i + j - k be two vectors. If c is a vector such that b c = b a and c a = 0, then c b is
- Let x_0 be the point of local minima of f(x) = a ( b c ) where a = x i - 2 j + 3 k , b = -2 i + x j - k , c = 7 i - 2 j + x k ,...
- If | a | = 3 ; | b | = 5; b c = 10, angle between b and c is 3 , a is perpendicular to b c . Then the value of | a ( b c )| is
- A vector parallel to the line of intersection of the planes r (3 i - j + k ) = 1 and r ( i + 4 j - 2 k ) = 2 is
- If a, b, c are three vectors such that | a+ b+ c|=1, c= ( a b) and | a|= 1 3 ,| b|= 1 2 ,| c|= 1 6 , then the angle between a and...
- If a, b, c are unit vectors and is angle between a and c and a+2 b+2 c= 0, then | a c|=
- If a, b, c are three vectors with magnitudes 3,1,2 respectively, such that a ( a c)+3 b= 0, if is the angle between a and c, then...
- Consider the lines L_1: x+1 3 = y+2 1 = z+1 2 , L_2: x-2 1 = y+2 2 = z-3 3 , then the unit vector perpendicular to both L_1 and...
- Let a= i+2 j-2 k and b= i- j+ k. If c is a vector such that a c=| c|, | c- a|=2 2 and the angle between a b and c is 60^0, then...
- Let ABCD be a quadrilateral with AB = a, AD = b, and AC =3 a+2 b. If its area is times the area of the parallelogram with AB, AD...
- The altitude of the parallelopiped, whose coterminous edges are the vectors a= i+ j+ k, b=2 i+4 j- k, c= i+ j+3 k, where a, b are...
- If a+ b+ c=0, | a|=| b|=| c|=3 and is the angle between b and c then ^2 + ^2 =
- A unit vector coplanar with i+ j+2 k and i+2 j+ k and perpendicular to i+ j+ k is
- Let ( p q ) denote the angle between p and q . If a + b + c = 0 , | a |=7, | b |=5 and | c |=3 then (take = 22 7 )
- If ABCDEF is a regular hexagon and AB + AC + AD + AE + AF =p AD =q AO , where O is the center of the hexagon, then the values of...
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