Advertisements
Advertisements
प्रश्न
Find the angle between the line `vec"r" = (2hat"i" - hat"j" + hat"k") + "t"(hat"i" + 2hat"j" - 2hat"k")` and the plane `vec"r"*(6hat"i" + 3hat"j" + 2hat"k")` = 8
उत्तर
`vec"b" = hat"i" + 2hat"j" - 2hat"k"`
`vec"n" = 6hat"i" + 3hat"j" + 2hat"k"`
`vec"b"*vec"n"` = 6 + 6 – 4 = 8
`|vec"b"| = sqrt(1 + 4 + 4) = sqrt(9)` = 3
`|vec"n"| = sqrt(36 + 9 + 4) = sqrt(49)` = 7
sin θ = `(|vec"b"*vec"n"|)/(|vec"b"||vec"n"|)`
= `8/(3 xx 7)`
= `8/21`
θ = `sin^-1(8/21)`
APPEARS IN
संबंधित प्रश्न
Find the equation of the plane passing through the line of intersection of the planes `vec"r"*(2hat"i" - 7hat"j" + 4hat"k")` = 3 and 3x – 5y + 4z + 11 = 0, and the point (– 2, 1, 3)
Find the equation of the plane passing through the line of intersection of the planes x + 2y + 3z = 2 and x – y + z = 3 and at a distance `2/sqrt(3)` from the point (3, 1, –1)
Find the angle between the planes `vec"r"*(hat"i" + hat"j" - 2hat"k")` = 3 and 2x – 2y + z = 2
Find the equation of the plane which passes through the point (3, 4, –1) and is parallel to the plane 2x – 3y + 5z + 7 = 0. Also, find the distance between the two planes
Find the length of the perpendicular from the point (1, – 2, 3) to the plane x – y + z = 5
Find the point of intersection of the line with the plane (x – 1) = `y/2` = z + 1 with the plane 2x – y – 2z = 2. Also, the angle between the line and the plane
Find the co-ordinates of the foot of the perpendicular and length of the perpendicular from the point (4, 3, 2) to the plane x + 2y + 3z = 2.
Choose the correct alternative:
If `vec"a" = hat"i" + hat"j" + hat"k", vec"b" = hat"i" + hat"j", vec"c" = hat"i"` and `(vec"a" xx vec"b")vec"c" - lambdavec"a" + muvec"b"` then the value of λ + µ is
