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प्रश्न
Choose the correct alternative:
I`vec"a" xx (vec"b" xx vec"c") = (vec"a" xx vec"b") xx vec"c"`, where `vec"a", vec"b", vec"c"` are any three vectors such that `vec"b"*vec"c" ≠ 0` and `vec"a"*vec"b" ≠ 0`, then `vec"a"` and `vec"c"` are
पर्याय
perpendicular
parallel
inclined at an angle `pi/3`
inclined at an angle `pi/6`
उत्तर
parallel
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संबंधित प्रश्न
Find the non-parametric form of vector equation and Cartesian equations of the straight line passing through the point with position vector `4hat"i" + 3hat"j" - 7hat"k"` and parallel to the vector `2hat"i" - 6hat"j" + 7hat"k"`
Find the direction cosines of the straight line passing through the points (5, 6, 7) and (7, 9, 13). Also, find the parametric form of vector equation and Cartesian equations of the straight line passing through two given points
Find the acute angle between the following lines.
`(x + 4)/3 = (y - 7)/4 = (z + 5)/5, vec"r" = 4hat"k" + "t"(2hat"i" + hat"j" + hat"k")`
Find the acute angle between the following lines.
2x = 3y = – z and 6x = – y = – 4z
f the straight line joining the points (2, 1, 4) and (a – 1, 4, – 1) is parallel to the line joining the points (0, 2, b – 1) and (5, 3, – 2) find the values of a and b
If the straight lines `(x - 5)/(5"m" + 2) = (2 - y)/5 = (1 - z)/(-1)` and x = `(2y + 1)/(4"m") = (1 - z)/(-3)` are perpendicular to ech other find the value of m
Show that the points (2, 3, 4), (– 1, 4, 5) and (8, 1, 2) are collinear
Find the parametric form of vector equation and Cartesian equations of straight line passing through (5, 2, 8) and is perpendicular to the straight lines `vec"r" = (hat"i" + hat"j" - hat"k") + "s"(2hat"i" - 2hat"j" + hat"k")` and `vec"r" = (2hat"i" - hat"j" - 3hat"k") + "t"(hat"i" + 2hat"j" + 2hat"k")`
Show that the lines `vec"r" = (6hat"i" + hat"j" + 2hat"k") + "s"(hat"i" + 2hat"j" - 3hat"k")` and `vec"r" = (3hat"i" + 2hat"j" - 2hat"k") + "t"(2hat"i" + 4hat"j" - 5hat"k")` are skew lines and hence find the shortest distance between them
Show that the lines `(x - 3)/3 = (y - 3)/(-1), z - 1` = 0 and `(x - 6)/2 = (z - 1)/3, y - 2` = 0 intersect. Aslo find the point of intersection
Show that the straight lines x + 1 = 2y = – 12z and x = y + 2 = 6z – 6 are skew and hence find the shortest distance between them
Find the parametric form of vector equation of the straight line passing through (−1, 2, 1) and parallel to the straight line `vec"r" = (2hat"i" + 3hat"j" - hat"k") + "t"(hat"i" - 2hat"j" + hat"k")` and hence find the shortest distance between the lines
Find the foot of the perpendicular drawn: from the point (5, 4, 2) to the line `(x + 1)/2 = (y - 3)/3 = (z - 1)/(-1)`. Also, find the equation of the perpendicular
Choose the correct alternative:
The vector equation `vec"r" = (hat"i" - hat"j" - hat"k") + "t"(6hat"i" - hat"k")` represents a straight line passing through the points
