Vector Algebra questions
907 published questions with worked solutions.
- ( a b) ( c d) is equal to
- If a, b, c, d are any four vectors then ( a b) ( c d) is a vector
- P is a point in the plane of the ABC whose orthocentre is H and the circumcentre is O. Forces AP , BP , CP and PH act at P. The...
- Three forces P, Q and R, each of 15 units, act along AB, BC and CA respectively. The position vectors of A, B and C are OA =2 i-...
- The vertices of a triangle ABC are A(-1,0,2), B(1,2,0) and C(2,3,4). The moment of a force of magnitude 10 acting at A along AB...
- The vector moment about the point i+2 j+3 k of the resultant of the forces i-2 j+5 k and 3 j-4 k acting at the point -2 i+3 j- k...
- The resolved parts of the force vector 5 i+4 j+2 k along and perpendicular to the vector 3 i+4 j-5 k are u and v respectively....
- If A = (1, 2, 3), B = (-2, 4, ) and AOB = /2 where O is the origin then is
- The volume of the tetrahedron whose vertices are (0, 1, 2), (4, 3, 6), (2, 3, 2) and (3, 0, 1) is (in unit^3)
- If (1, -1, 0), (-2, 1, 8) and (-1, 2, 7) are three consecutive vertices of a parallelogram then the fourth vertex is
- If A = (2, -3, 7), B = (-1, 4, -5) and P is a point on the line AB such that AP : BP = 3 : 2 then P has the coordinates
- The shortest distance between the line x-3 3 = y 0 = z -4 and the y-axis is
- The equations of the line of shortest distance between the lines x+4 4 = y-2 -2 = z-3 0 and x-5 5 = y-3 3 = z0 are
- The distance between the lines x-4 2 = y+1 -3 = z6 and x -1 = y-1 3/2 = z+1 -3 is
- The shortest distance between the lines x-y=0=2x+z and x+y-2=0=3x-y+z-1 is
- The shortest distance between the lines whose equations are r=t( i+ j+ k) and r= k+s( i-2 j+3 k) is
- If a, b are orthogonal unit vectors then for a vector r, noncoplanar with a and b, the vector r a is equal to
- Let f(t)=[t] , i+(t-[t]) , j+[t+1] , k, where [ ] denotes the greatest integer function. Then the vectors f ( 54 ) and f(t),...
- If a, b, c are three vectors such that | a|=| c|=1, | b|=4, | b c|=2 and 2 b= c+ a then is
- Let a , b , c be unit vectors and , , are angles between the vectors a , b ; b , c and c , a respectively. If a + b + c is also a...
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