M L Aggarwal Solutions for Chapter: Determinants, Exercise 3: EXERCISE 4.3

Show that the points $(1, 0), (6, 0), (0, 0)$ are collinear.

Using determinants, determine whether the points $\mathrm{P}(a, b+c), \mathrm{Q}(b, c+a)$ and $\mathrm{R}(c, a+b)$ form a triangle or not.

Using determinants, find the value of $\lambda$ so that the points $(\lambda , 7), (1,-5)$ and $(-4, 5)$ are collinear.

 Using determinants, find the equation of the line passing through the points $\left(1, 2\right)$ and $\left(3, 6\right)$.

If the area of triangle with vertices $(-3, 0), (3, 0)$ and $(0, k)$ is $9$ Sq. Units, find the value of $k$.

Find the value(s) of $k$ if the area of the triangle with vertices $(k, 0), (4, 0)$ and $(0, 2)$ is $4$ square units.

Find the value(s) of $x$ if the area of the triangle with vertices $(x, 4), (2, -6)$ and $(5, 4)$ is $35$ square units.

Points $\left(a, 0\right), \left(0, b\right), \left(1, 1\right)$ are collinear. Prove that $a+b=ab$.