HSC Arts Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions

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

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

Sketch the graphs of the following functions

y = `- 1/3 (x^3 - 3x + 2)`

Sketch the graphs of the following functions:

y = `xsqrt(4 - x)`

Sketch the graphs of the following functions:

y = `(x^2 + 1)/(x^2 - 4)`

Sketch the graphs of the following functions:

y = `1/(1 + "e"^-x)`