Advertisements
Advertisements
प्रश्न
Choose the correct alternative:
If a vector `vecalpha` lies in the plane of `vecbeta` and `vecϒ`, then
विकल्प
`[vecalpha, vecbeta, vecϒ]` = 1
`[vecalpha, vecbeta, vecϒ]` = – 1
`[vecalpha, vecbeta, vecϒ]` = 0
`[vecalpha, vecbeta, vecϒ]` = 2
उत्तर
`[vecalpha, vecbeta, vecϒ]` = 0
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 an angle in a semi-circle is a right angle
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)
Prove by vector method that sin(α + ß) = sin α cos ß + cos α sin ß
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
Forces of magnitudes `5sqrt(2)` and `10sqrt(2)` units acting in the directions `3hat"i" + 4hat"j" + 5hat"k"` and `10hat"i" + 6hat"j" - 8hat"k"` respectively, act on a particle which is displaced from the point with position vector `4hat"i" - 3hat"j" - 2hat"k"` to the point with position vector `6hat"i" + hat"j" - 3hat"k"`. Find the work done by the forces
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 `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 `veca = αhati + 3hatj - hatk, vecb = 3hati - βhatj + 4hatk` and `vecc = hati + 2hatj - 2hatk` where α, β ∈ R, be three vectors. If the projection of a `veca` on `vecc` is `10/3` and `vecb xx vecc = -6hati + 10hatj + 7hatk`, then the value of α + β is equal to ______.
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 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 ______.