Advertisements
Advertisements
प्रश्न
A particle acted on by constant forces `8hat"i" + 2hat"j" - 6hat"k"` and `6hat"i" + 2hat"j" - 2hat"k"` is displaced from the point (1, 2, 3) to the point (5, 4, 1). Find the total work done by the forces
उत्तर
`bar"OA" = hat"i" + 2hat"j" + 3hat"k"`
`bar"OB" = 5hat"i" + 4hat"j" + hat"k"`
`bar"d" = bar"AB"`
= `bar"OB" - bar"OA"`
= `4hat"i" + 2hat"j" - 2hat"k"`
`bar"F"_1 = 8hat"i" + 2hat"j" - 6hat"k"`
And `bar"F"_2 = 6hat"i" + 2hat"j" - 2hat"k"`
`bar"F" = bar"F"_1 + bar"F"_2`
= `14hat"i" + 4hat"j" - 8hat"k"`
Work done = `bar"F" bar"d"`
= `(14hat"i" + 4hat"j" - 8hat"k")(4hat"i" + 2hat"j" - 2hat"k")`
= 56 + 8 + 16
= 80 units
APPEARS IN
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 the diagonals of a rhombus bisect each other at right angles
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 sin(α + ß) = sin α cos ß + cos α sin ß
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"`
Choose the correct alternative:
If `vec"a"` and `vec"b"` are parallel vectors, then `[vec"a", vec"c", vec"b"]` is equal to
Choose the correct alternative:
If a vector `vecalpha` lies in the plane of `vecbeta` and `vecϒ`, then
Choose the correct alternative:
If `vec"a"*vec"b" = vec"b"*vec"c" = vec"c"*vec"a"` = 0, then the value of `[vec"a", vec"b", vec"c"]` is
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 = hati - 2hatj + 3hatk, vecb = hati + hatj + hatk` and `vecc` be a vector such that `veca + (vecb xx vecc) = vec0` and `vecb.vecc` = 5. Then, the value of `3(vecc.veca)` is equal to ______.
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`
The vector `vecp` perpendicular to the vectors `veca = 2hati + 3hatj - hatk` and `vecb = hati - 2hatj + 3hatk` and satisfying the condition `vecp.(2hati - hatj + hatk)` = –6 is ______.
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 ______.
