Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

Classify the following measures as scalar and vector.

10 kg

Classify the following as scalar and vector quantity.

Time period

In Figure, identify the following vector.

Coinitial

`veca and -veca` are collinear.

Two collinear vectors are always equal in magnitude.

Two vectors having the same magnitude are collinear.

Two collinear vectors having the same magnitude are equal.

Find the direction cosines of the vector `hati + 2hatj + 3hatk`.

Find the direction cosines of the vector joining the points A (1, 2, -3) and B (-1, -2, 1) directed from A to B.

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are  `hati + 2hatj - hatk` and `-hati + hatj + hatk`  respectively, externally in the ratio 2:1.

Show that the points A, B and C with position vectors `veca = 3hati - 4hatj - 4hatk`, `vecb = 2hati - hatj + hatk` and `vecc = hati - 3hatj - 5hatk`, respectively form the vertices of a right angled triangle.

Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of the x-axis.

Find the value of x for which `x(hati + hatj + hatk)` is a unit vector.

If θ is the angle between two vectors `veca` and `vecb`, then `veca . vecb >= 0` only when ______.

Let `veca` and `vecb` be two unit vectors, and θ is the angle between them. Then `veca + vecb` is a unit vector if ______.

Determine the order and degree (if defined) of the differential equation:

`(d^4y)/(dx^4) + sin(y^("')) = 0`

Determine the order and degree (if defined) of the differential equation:

y' + 5y = 0

Determine the order and degree (if defined) of the differential equation:

`((ds)/(dt))^4 + 3s  (d^2s)/(dt^2) = 0`