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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`
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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 parametric form of vector equation and Cartesian equations of the straight line passing through the point (– 2, 3, 4) and parallel to the straight line `(x - 1)/(-4) = (y + 3)/5 = (8 - z)/6`
Find the points where the straight line passes through (6, 7, 4) and (8, 4, 9) cuts the xz and yz planes
Find the acute angle between the following lines.
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Find the acute angle between the following lines.
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Find the acute angle between the following lines.
2x = 3y = – z and 6x = – y = – 4z
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
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
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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
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Choose the correct alternative:
If `vec"a", vec"b", vec"c"` are non-coplanar, non-zero vectors `[vec"a", vec"b", vec"c"]` = 3, then `{[[vec"a" xx vec"b", vec"b" xx vec"c", vec"c" xx vec"a"]]}^2` is equal to
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
