Vector Algebra questions
907 published questions with worked solutions.
- One or more may match with the same. Column I: (i) In an acute-angled ABC, the minimum value of A + B + C is (ii) _ x 0 0 x^2 + y...
- If a b = 1 and a b = j - k, where a = i + j + k, then b is
- The unit vector which is orthogonal to the vector a = 3 i + 2 j + 6 k and is coplanar with the vectors b = 2 i + j + k and c = i...
- If the vectors a, b and c are represented by the sides BC, CA and AB, respectively, of the ABC then
- If a, b and c are unit coplanar vectors then the scalar triple product [2 a - b ; ; 2 b - c ; ; 2 c - a] is equal to
- Let the vectors a, b, c and d be such that ( a b) ( c d) = 0. Let P_1 and P_2 be planes determined by pairs of vectors a, b and...
- Let a = i + 2 j + k, b = i - j + k and c = i + j - k. A vector in the plane of a and b whose projection on c is 1 3 is
- If a, b and c are unit vectors then | a - b|^2 + | b - c|^2 + | c - a|^2 does not exceed
- Let a = i - k, b = x i + j + (1-x) k and c = y i + x j + (1 + x - y) k. Then [ a b c] depends on
- Let A be a vector parallel to the line of intersection of the planes P_1 and P_2 through the origin. The plane P_1 is parallel to...
- If a and b are two unit vectors such that a + 2 b and 5 a - 4 b are perpendicular to each other then the angle between a and b is
- Let V = 2 i + j - k and W = i + 3 k. If U is a unit vector then the maximum value of the scalar triple product [ U V W] is
- The number of distinct real values of , for which the vectors - ^2 i + j + k, i - ^2 j + k and i + j - ^2 k are coplanar, is
- The edges of a parallelopiped are of unit length and are parallel to noncoplanar unit vectors a, b, c such that a b = b c = c a =...
- Let two non-collinear unit vectors a and b form an acute angle. A point P moves so that at any time t the position vector OP...
- If a, b, c and d are unit vectors such that ( a b) ( c d) = 1 and a c = 12 then
- Let P, Q, R and S be points on the plane with position vectors -2 i - j, 4 i, 3 i + 3 j and -3 i + 2 j respectively. The...
- Two adjacent sides of a parallelogram ABCD are given by AB = 2 i + 10 j + 11 k and AD = - i + 2 j + 2 k. The side AD is rotated...
- If a and b are vectors in space given by a = i - 2 j 5 and b = 2 i + j + 3 k 14 then the value of (2 a + b) [( a b) ( a - 2 b) ]...
- Let a = i + j + k, b = i - j + k and c = i - j - k. A vector v in the plane of a and b, whose projection on c is 1 3 , is given by
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