Vector Algebra questions
907 published questions with worked solutions.
- If a , b and c are coplanar, then what is (2 a 3 b ) 4 c +(5 b 3 c ) 6 a equal to?
- Consider the following statements : 1. The cross product of two unit vectors is always a unit vector. 2. The dot product of two...
- The xy-plane divides the line segment joining the points (-1, 3, 4) and (2, -5, 6)
- Let a , b and c be unit vectors such that a b is perpendicular to c . If is the angle between a and b , then which of the...
- If a +3 b =3 i - j and 2 a + b = i -2 j , then what is the angle between a and b ?
- Let a , b and c be three vectors such that a , b and c are coplanar. Which of the following is/are correct? 1. ( a b ) c is...
- If the position vectors of A and B are ( 2 -1) i - j and i +( 2 +1) j respectively, then what is the magnitude of AB ?
- In a triangle PQR, let a = QR , b = RP and c = PQ . If | a | = 3, | b | = 4 and a ( c - b ) c ( a - b ) = | a | | a |+| b | ,...
- Let a and b be positive real numbers. Suppose PQ = a i + b j and PS = a i - b j are adjacent sides of a parallelogram PQRS. Let u...
- Let u , v and w be vectors in three-dimensional space, where u and v are unit vectors which are not perpendicular to each other...
- Let O be the origin and OA = 2 i + 2 j + k , OB = i - 2 j + 2 k and OC = 1 2 ( OB - OA ) for some > 0. If | OB OC | = 9 2 , then...
- Let i , j and k be the unit vectors along the three positive coordinate axes. Let a = 3 i + j - k , b = i + b_2 j + b_3 k , b_2,...
- Let Q be the cube with the set of vertices (x_1, x_2, x_3) R ^3 : x_1, x_2, x_3 0, 1 . Let F be the set of all twelve lines...
- Let P be the plane 3 x + 2y + 3z = 16 and let S = i + j + k : ^2 + ^2 + ^2 = 1 and the distance of ( , , ) from the plane P is 7...
- Let the position vectors of the points P, Q, R and S be a = i + 2 j - 5 k , b = 3 i + 6 j + 3 k , c = 17 5 i + 16 5 j + 7 k and d...
- Let OP = - 1 i + j + k , OQ = i + - 1 j + k and OR = i + j + 1 2 k be three vectors, where , R - 0 and O denotes the origin. If (...
- Let p = 2 i + j + 3 k and q = i - j + k . If for some real numbers , , and , we have 15 i + 10 j + 6 k = (2 p + q ) + ( p - 2 q )...
- Let a , b , c be three non-coplanar vectors such that a b = 4 c , b c = 9 a and c a = b , > 0. If | a | + | b | + | c | = 1/36,...
- Let a = i + j + k and b = 3 i - 5 j + 4 k be two vectors, such that a b = - i + 9 j + 12 k . Then the projection of b - 2 a on b...
- Let a = 2 i - j + 5 k and b = i + j + 2 k . If (( a b ) i ) k = 23/2, then | b 2 j | is equal to
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