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प्रश्न
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
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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 points where the straight line passes through (6, 7, 4) and (8, 4, 9) cuts the xz and yz planes
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.
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The vertices of ΔABC are A(7, 2, 1), 5(6, 0, 3), and C(4, 2, 4). Find ∠ABC
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
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
If the two lines `(x - 1)/2 = (y + 1)/3 = (z - 1)/4` and `(x - 3)/1 = (y - "m")/2` = z intersect at a point, find the value of m
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
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
