Vector Algebra questions
907 published questions with worked solutions.
- The vector and Cartesian equation of the line which passes through the point (1, 2, 3) and is parallel to the vector i - 2 j + 3...
- The vector equation of the line x - 5 3 = y + 4 7 = z - 6 2 is
- The vector equation of the line, whose cartesian equation is x - 3 2 = y + 4 5 = z - 6 3 is
- Lines r = (2 i - 3 j + 7 k ) + (2 i + p j + 5 k ) and r = (p i + 2 j + 3 k ) + (3 i - p j + p k ) are perpendicular for all...
- Let a = i + j and b = 2 i - k , then the point of intersection of the lines r a = b a and r b = a b is
- The vector equation of the line through the points (-1, 0, 2) and (3, 4, 6) is
- Find the vector and the cartesian equations of the line through the point (5, 2, -4) and which is parallel to the vector 3 i + 2...
- The vector equation of the line x + 2 3 = 1 - y 2 = z - 5 7 is
- Equation of a line passing through the point with position vector 2 i - 3 j + 4 k and in the direction of the vector 3 i + 4 j -...
- The shortest distance between lines r = ( i - j ) + (2 i + k ) and r = (2 i - j ) + ( i - j - k ) is
- The shortest distance between lines r = (1 - t) i + (t - 2) j + (3 - t) k and r = (s + 1) i + (2s - 1) j - (2s + 1) k is
- The shortest distance between the lines r = (4 i - j ) + ( i + 2 j - 3 k ) and r = ( i - j + 2 k ) + (2 i + 4 j - 5 k ) is
- The shortest distance between the lines x - 1 2 = y - 2 3 = z - 3 4 and x - 2 3 = y - 4 4 = z - 5 5 is
- The shortest distance between lines r = ( - 1) i + ( + 1) j - (1 + ) k and r = (1 - ) i + (2 - 1) j + ( + 2) k is
- The vector equation r = i - 2 j - k + t(6 j - k ), represents a line passing through points
- Consider the lines: L_1: x + 1 3 = y + 2 1 = z + 1 2 , L_2: x - 2 1 = y + 2 2 = z - 3 3 . The unit vector perpendicular to both...
- A square ABCD of diagonal 2a is folded along the diagonal AC so that the planes DAC and BAC are at right angle. The shortest...
- The unit vector perpendicular to both L_1: x + 1 3 = y + 2 1 = z + 1 2 and L_2: x - 2 1 = y + 2 2 = z - 3 3 is
- The shortest distance between lines L_1: x + 1 3 = y + 2 1 = z + 1 2 , L_2: x - 2 1 = y + 2 2 = z - 3 3 is
- The shortest distance between the lines x - 3 3 = y - 8 -1 = z - 3 1 and x + 3 -3 = y + 7 2 = z - 6 4 is
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