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Choose the correct alternative: If aa→ and bb→ are parallel vectors, then acb[a→,c→,b→] is equal to - Mathematics

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प्रश्न

Choose the correct alternative:

If `vec"a"` and `vec"b"` are parallel vectors, then `[vec"a", vec"c", vec"b"]` is equal to

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shaalaa.com
Scalar Product and Vector Product
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Applications of Vector Algebra - Exercise 6.10 [पृष्ठ २७६]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
पाठ 6 Applications of Vector Algebra
Exercise 6.10 | Q 1 | पृष्ठ २७६

संबंधित प्रश्‍न

Prove by vector method that if a line is drawn from the centre of a circle to the midpoint of a chord, then the line is perpendicular to the chord


Prove by vector method that the median to the base of an isosceles triangle is perpendicular to the base


Prove by vector method that an angle in a semi-circle is a right angle


Prove by vector method that the diagonals of a rhombus bisect each other at right angles


Using vector method, prove that if the diagonals of a parallelogram are equal, then it is a rectangle


Prove by vector method that the area of the quadrilateral ABCD having diagonals AC and BD is `1/2 |bar"AC" xx bar"BD"|`


Prove by vector method that the parallelograms on the same base and between the same parallels are equal in area


If G is the centroid of a ΔABC, prove that (area of ΔGAB) = (area of ΔGBC) = (area of ΔGCA) = `1/3` (area of ΔABC)


Using vector method, prove that cos(α – β) = cos α cos β + sin α sin β


Find the magnitude and direction cosines of the torque of a force represented by `3hat"i" + 4hat"j" - 5hat"k"` about the point with position vector `2hat"i" - 3hat"j" + 4hat"k"`  acting through a point whose position vector is `4hat"i" + 2hat"j" - 3hat"k"`


Find the torque of the resultant of the three forces represented by `- 3hat"i" + 6hat"j" - 3hat"k", 4hat"i" - 10hat"j" + 12hat"k"` and `4hat"i" + 7hat"j"` acting at the point with position vector `8hat"i" - 6hat"j" - 4hat"k"` about the point with position vector `18hat"i" + 3hat"j" - 9hat"k"`


Let A, B, C be three points whose position vectors respectively are 

`vec"a" = hat"i" + 4hat"j" + 3hat"k"`

`vec"b" = 2hat"i" + αhat"j" + 4hat"k", α ∈ "R"`

`vec"c" = 3hat"i" - 2hat"j" + 5hat"k"`

If α is the smallest positive integer for which `vec"a", vec"b", vec"c"` are noncollinear, then the length of the median, in ΔABC, through A is ______.


Let `veca = 2hati + hatj - 2hatk` and `vecb = hati + hatj`. If `vecc` is a vector such that `veca.vecc = |vecc|, |vecc - veca| = 2sqrt(2)`, angle between `(veca xx vecb)` and `vecc` is `π/6`, then the value of `|(veca xx vecb) xx vecc|` is ______.


Let `veca, vecb, vecc` be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle θ, with the vector `veca + vecb + vecc`. Then, 36 cos22θ is equal to ______.


Let `veca, vecb` and `vecc` be three unit vectors such that `|veca - vecb|^2 + |veca - vecc|^2` = 8. Then find the value of `|veca + 2vecb|^2 + |veca + 2vecc|^2`


Let a, b, c ∈ R be such that a2 + b2 + c2 = 1. If `a cos θ = b cos(θ + (2π)/3) = c cos(θ + (4π)/3)`, where θ = `π/9`, then the angle between the vectors `ahati + bhatj + chatk` and `bhati + chatj + ahatk` is ______.


If `vecx` and `vecy` be two non-zero vectors such that `|vecx + vecy| = |vecx|` and `2vecx + λvecy` is perpendicular to `vecy`, then the value of λ is ______.


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