Vector Algebra questions
907 published questions with worked solutions.
- The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors a , b , c such that a b = b c = c...
- If the vectors AB = 3 i + 4 k and AC = 5 i - 2 j + 4 k are the sides of a triangle ABC, then the length of the median through A...
- Let a = - i + 2 j + 2 k , b = 8 i + 7 j - 3 k and c be a vector such that a c = b . If c ( i + j + k ) = 4, then | a + c |^2 is...
- Let c and d be vectors such that | c + d | = 29 and c (2 i + 3 j + 4 k ) = (2 i + 3 j + 4 k ) d . If _1, _2 ( _1 > _2) are the...
- For a triangle ABC, let p = BC , q = CA and r = BA . If | p | = 2 3 , | q | = 2 and = 1 3 , where is the angle between p and q ,...
- Let AB = 2 i + 4 j - 5 k and AD = i + 2 j + k , R . Let the projection of the vector v = i + j + k on the diagonal AC of the...
- Let a = 2 i - j + k and b = j +2 k , Z be two vectors, Let c = a b and d be a vector of magnitude 2 in yz-plane. If | c | = 53 ,...
- Let a vector a = 2 i - j + k , >0, make an obtuse angle with the vector b =- ^2 i +4 2 j +4 2 k and an angle , 6 < < 2 , with the...
- Let a = - i + j +2 k , b = i - j -3 k , c = a b and d = c a . Then ( a - b ) d is equal to :
- Let a = i - 2 j + 3 k , b = 2 i + j - k , c = i + j + k and v = a b . If v c = 11 and the length of the projection of b on c is...
- Let a , b , c be three vectors such that a b = 2( a c ). If | a | = 1, | b | = 4, | c | = 2, and the angle between b and c is 60^...
- Let a = 2 i + j -2 k , b = i + j and c = a b . Let d be a vector such that | d - a | = 11 , | c d | = 3 and the angle between c...
- The sum of all values of , for which the shortest distance between the lines x+1 = y-2 -1 = z-4 - and x = y-1 2 = z-1 2 is 2 , is
- Let a = 2 i -5 j +5 k and b = i - j +3 k . If c is a vector such that 2( a c )+3( b c )= 0 and ( a - b ) c =-97, then | c k |^2...
- For three unit vectors a , b , c satisfying | a - b |^2+| b - c |^2+| c - a |^2 = 9 and |2 a +k b +k c | = 3, the positive value...
- Let L1 : x-1 2 = y-2 3 = z-3 4 and L2 : x-2 3 = y-4 4 = z-5 5 be two lines. Then which of the following points lies on the line...
- Let c be the projection vector of b = i +4 k , λ > 0, on the vector a = i +2 j +2 k . If | a + c | = 7, then the area of the...
- Let a and b be two unit vectors such that the angle between them is 3 . If a +2 b and 3 a - b are perpendicular to each other,...
- Let the point A divide the line segment joining the points P(–1, –1, 2) and Q(5, 5,10) internally in the ratio r : 1 (r > 0). If...
- If the square of the shortest distance between the lines x-2 1 = y-1 2 = z+3 -3 and x+1 2 = y+3 4 = z+5 -5 is m n , where m, n...
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