मराठी
तामिळनाडू बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान इयत्ता १२

Choose the correct alternative: Iabcabca→× (b→×c→)=(a→×b→)×c→, where abca→,b→,c→ are any three vectors such that bcb→⋅c→≠0 and aba→⋅b→≠0, then aa→ and cc→ are - Mathematics

Advertisements
Advertisements

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`

MCQ
Advertisements

उत्तर

parallel

shaalaa.com
Application of Vectors to 3-dimensional Geometry
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Applications of Vector Algebra - Exercise 6.10 [पृष्ठ २७७]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
पाठ 6 Applications of Vector Algebra
Exercise 6.10 | Q 13 | पृष्ठ २७७

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.

`vec"r" = (4hat"i" - hat"j") + "t"(hat"i" + 2hat"j" - 2hat"k")`


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")`


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


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


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:

If `[vec"a", vec"b", vec"c"]` = 1, then the value of `(vec"a"*(vec"b" xx vec"c"))/((vec"c" xx vec"a")*vec"b") + (vec"b"*(vec"c" xx vec"a"))/((vec"a" xx vec"b")*vec"c") + (vec"c"*(vec"a" xx vec"b"))/((vec"c" xx vec"b")*vec"a")` is


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×