Vector Algebra questions
907 published questions with worked solutions.
- Let a = i + 2 j + 3 k , b = 3 i + j - k and c be three vectors such that c is coplanar with a and b . If the vector c is...
- Let a = i + j + k , b = 2 i +2 j + k and d = a b . If c is a vector such that a . c = | c |, | c -2 a |^2 = 8 and the angle...
- Let A, B, C be three points in xy-plane, whose position vectors are given by 3 i + j , i + 3 j and a i +(1-a) j respectively with...
- If the components of a = i + j + k along and perpendicular to b =3 i + j - k respectively, are 16 11 (3 i + j - k ) and 1 11 (-4...
- Let a = 2 i - j + 3 k , b = 3 i - 5 j + k and c be a vector such that a c = c b and ( a + c ).( b + c ) = 168. Then the maximum...
- Let a = i + 2 j + k and b = 2 i + 7 j + 3 k . Let L_1 : r = (- i + 2 j + k ) + a , R and L_2 : r = ( j + k ) + b , R be two...
- The line L_1 is parallel to the vector a = -3 i + 2 j + 4 k and passes through the point (7, 6, 2) and the line L_2 is parallel...
- Let a = 2 i - 3 j + k , b = 3 i + 2 j + 5 k and a vector c be such that ( a - c ) b = -18 i - 3 j + 12 k and a c = 3. If b c = d...
- If a is a non-zero vector such that its projections on the vectors 2 i - j + 2 k, i + 2 j - 2 k and k are equal, then a unit...
- Let a = i + 2 j + k , b = 3 i - 3 j + 3 k , c = 2 i - j + 2 k and d be a vector such that b d = c d and a . d = 4. Then | a d |^2...
- Let a = i+ j+ k, b = 3 i+2 j- k, c = j+ k and d be a unit vector such that a d = b d and c. d = 1. If c is perpendicular to a,...
- Consider two vectors u = 3 i - j and v = 2 i + j - k , λ > 0. The angle between them is given by ^ -1 ( 5 2 7 ). Let v = v_1 +...
- Let the shortest distance between the lines x-3 3 = y- -1 = z-3 1 and x+3 -3 = y+7 2 = z- 4 be 3 30 . Then the positive value of...
- Let a = i + 2 j + k and b = 2 i + j - k . Let c be a unit vector in the plane of the vector a and b and be perpendicular to a ....
- Let the value of for which the shortest distance between the lines x-1 2 = y-2 3 = z-3 4 and x- 3 = y-4 4 = z-5 5 is 1 6 be _1...
- Let the values of p, for which the shortest distance between the lines x+1 3 = y 4 = z 5 and r = (p i + 2 j + k ) + (2 i + 3 j +...
- Let a and b be the vectors of the same magnitude such that | a + b |+| a - b | | a + b |-| a - b | = 2 +1. Then | a + b |^2 | a...
- If [ a b b c c a ] = [ a b c ]^2 then is equal to:
- Let a , b and c be three unit vectors such that a ( b c ) = 3 2 ( b c ). If b is not parallel to c , then the angle between a and...
- Let a = 2 i + j - 2 k and b = i + j . Let c be a vector such that | c - a | = 3, |( a b ) c | = 3 and the angle between c and a b...
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