Download App

Determinants — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDeterminants3 Marks
Question
Using determinants show that the following points are collinear:
$(3, -2), (8, 8)$ and $(5, 2)$
✓

Answer

If the points (3, -2), (8, 8) and (5, 2) collinear, then
$\triangle=\begin{vmatrix}3&-2&1\\8&8&1\\5&2&1\end{vmatrix}=0$
$=\begin{vmatrix}3&-2&1\\5&10&0\\5&2&1\end{vmatrix}$ [Applying $R_2 \rightarrow R_2 - R_1$]
$=\begin{vmatrix}3&-2&1\\5&10&0\\2&4&0\end{vmatrix}$ [Applying $R_3 \rightarrow R_3 - R_1$]
$=\begin{vmatrix}5&10\\2&4\end{vmatrix}$
$=20-20$
$=0$
Thus, points are collinear.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(3 Marks)" from Determinants→Determinants — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Evaluate the following:

$\int_0^1 \frac{1}{1+\sqrt{x}} d x$

→
Find the vector equation of the plane passing through the points A(1, -2, 1), B (2, -1, -3) and C (0, 1, 5).
→
Differentiate the following functions with respect to x:
$\text{e}^{\sin^{-1}2\text{x}}$
→
Solve the following equations by reduction method $: 2x + y = 5, 3x + 5y = -3$
→
Find the area of the parallelogram whose diagonals are:
$2\hat{\text{i}}+3\hat{\text{j}}+6\hat{\text{k}}$ and $3\hat{\text{i}}-6\hat{\text{i}}+2\hat{\text{k}}$
→
Evaluate the following integrals:$\int\limits^8_2|\text{x}-5|\text{dx}$
→
Differentiate the following w.r.t. x:

$\sin \left[2 \tan ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)\right]$

→
In $\Delta A B C$, if $a \cos A=b \cos B$ then prove that the triangle is either a right angled or an isosceles triangle.
→
Find fog and gof if:$f(x) = x^2 + 2$, $\text{g(x)}=1-\frac{1}{1-\text{x}}$
→
If $\text{y}=\log_\text{a}\text{x},$, find $\frac{\text{dy}}{\text{dx}}.$
→