Question

Write a unit vector in the direction of vector $\stackrel{\rightarrow}{PQ}\$ where $\stackrel{\rightarrow}{p}\$ and $\stackrel{\rightarrow}{q}\$ are the points (1, 3, 0) and (4, 5, 6),respectively,

If $\stackrel{\rightarrow}{a}\$ =$4\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $\stackrel{\rightarrow}{b}\$ =$2\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ then find a unit vector parallel to the vector $\stackrel{\rightarrow}{a}+\stackrel{\rightarrow}{b}$

Write the degree of the differential equation : $\left({\frac{d^{2}y}{d x^{2}}}\right)^{2}-2{\frac{d^{2}y}{d x^{2}}}-{\frac{d y}{d x}}+1=0.$

Find the solution of the differential equation ${\frac{d y}{d x}}=x^{3}e^{-2y}$.

State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive.

If A is an invertible square matrix of order 3 and |A| = 5, then find the value of |adj A|.

Write the equation of tangent drawn to the curve y = sin x at the point (0, 0).