Download App

DETERMINANTS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDETERMINANTS3 Marks
Question
Using determinants show that the following points are collinear:
(2, 3), (-1, -2) and (5, 8)
✓

Answer

If given points are collinear, then area of the triangle must be zero.
Hence,
$=\frac{1}{2}\begin{vmatrix}2&3&1\\-1&-2&1\\5&8&1\end{vmatrix}$
$=\frac{1}{2}\big[2(-10)-3(-6)+1(2)\big]$
$=\frac{1}{2}[-20+18+2]$
$=\frac{1}{2}[0]$
$=0$
Hence the given 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 "3 Marks Question" from DETERMINANTS→DETERMINANTS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

A plabne makes intercepts -6, 3, 4 respectively on the coordinate axes. Find the length of the perpendicular from the origin on it.
→
Solve:
$\sin\Big(\sin^{-1}\frac{1}{5}+\cos^{-1}\text{x}\Big)=1$
→
Solve the system of linear equation, using matrix method 5x + 2y = 4; 7x + 3y = 5
→
If A and B be two events such that $\text{P(A)}=\frac{1}{4},\text{P(B)}=\frac{1}{3}$ and $\text{P}(\text{A}\cap\text{B})=\frac{1}{2},$ show that A and B are independent events.
→
A binary operation $*$ is defined on the set $R$ of all real numbers by the rule $\text{a}\times\text{b}=\sqrt{\text{a}^2+\text{b}^2}\ \forall\text{ a, b}\in\text{R}$. Write the identity element for $*$ on $R$.
→
A manufacturer produces three products, x, y, z which he sells in two markets. Annual sales are indicated below:
Market Products
I 10000 2,000 18,000
II 6000 20,000 8,000
  1. If unit sale prices of x, y and z are Rs 2.50, Rs 1.50 and Rs 1.00 respectively, find the total revenue in each market with the help of matrix algebra.
  2. If the unit costs of the above three commodities are Rs 2.00, Rs 1.00 and 50 paise respectively. Find the gross profit.
→
Consider the binary operation * on the set {1, 2, 3, 4, 5} defined by a * b =min. {a, b}. Write the operation table of the operation *.
→
For what value of k is the following function continuous at x = 2?
$\text{f(x)}=\begin{cases}2\text{x}+1,&\text{if }\text{ x}<2\\\text{k},&\text{x}=2\\3\text{x}-1,&\text{x}>2\end{cases}$
→
Check the commutativity and associativity of the following binary operations:
'*' on Q defined by $\text{a}\ ^*\ \text{b}=\frac{\text{ab}}{4}$ for all a, b ∈ Q.
→
Find the equation of the plane passing through the origin and perpendicular to each of the planes x + 2y - z = 1 and 3x - 4y + z = 5.
→