Download App

Algebra of Vectors — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Vectors3 Marks
Question
Using vectors, find the value of $\lambda$ such that the points ($\lambda$, -10, 3), (1, -1, 3) and (3, 5, 3) are collinear.
✓

Answer

Points ($\lambda$, -10, 3), (1, -1, 3) and (3, 5, 3) are collinear.$\therefore$ ($\lambda$, -10, 3) = x(1, -1, 3) + y(3, 5, 3) for some scalars x and y.
$\Rightarrow\lambda$ = x + 3y, -10 = -x + 5y and 3 = 3x +3y
Solving -10 = -x + 5y and 3 = 3x + 3y for x and y we get,
$\text{x}=\frac{5}2$ and $\text{y}=-\frac{3}2$
Now,
$\lambda=\text{x}+3\text{y}$
$\Rightarrow\lambda=\frac{5}2+3\Big(-\frac{3}2\Big)=-2$

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 Algebra of Vectors→Algebra of Vectors — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

In $\triangle ABC$, prove that $\sin \left(\frac{ B - C }{2}\right)=\left(\frac{b-c}{a}\right) \cos \left(\frac{ A }{2}\right)$
→
A coin is tossed three times. Find $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)$ in each of the following:
A = At most two tails,
B = At least one tail.
→
$\int\frac{1+\cos\text{x}}{1-\cos\text{x}}\text{dx}$
→
Find the acute angle between lines $\frac{x-1}{1}=\frac{y-2}{-1}=\frac{z-3}{2}$ and $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-3}{1}$.
→
In the following, find the value of the constant k so that the given function is continuous at the indicated point:
$\text{f(x)}=\begin{cases}\text{k}+1,&\text{if}\text{ x}\leq5\\3\text{x}-5,&\text{if}\text{ x}>5\end{cases}\text{at x} =5$
→
Find the $n^{\text {th }}$ derivative of the following : $\log x$
→
The surface area of a spherical balloon is increasing at the rate of $2 cm ^2 / sec$. At what rate the volume of the balloon is increasing when the radius of the balloon is $6 cm$ ?
→
Evaluate the following integrals:
$\int5^{5^{5^{\text{x}}}}5^{5^{\text{x}}}5^\text{x}\text{ dx}$
→
Find the acute angle between the line $\bar{r}=\lambda(\hat{i}-\hat{j}+\hat{k})$ and the plane

$\bar{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=23$

→
Evaluate the following integrals:
$\int\frac{(1+\sqrt{\text{x}})^2}{\sqrt{\text{x}}}\text{dx}$
→