Download App

Scalar Or Dot Product — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsScalar Or Dot Product2 Marks
Question
Write the value of $\lambda$ so that vectora $\vec{\text{a}}=2\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}$ are perpendicular to each other.
✓

Answer

We have
$\vec{\text{a}}=2\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}$
The given vectors are perpendicular. so, their dot product is zero.
$\big(​​2\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}}\big).\big(\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}\big)$
$\Rightarrow2-2\lambda+3=0$
$\Rightarrow5-2\lambda=0$
$\Rightarrow-2\lambda=-5$
$\Rightarrow\lambda=\frac{5}{2}$

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.(2 Marks)" from Scalar Or Dot Product→Scalar Or Dot Product — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Solve the following differential equations.

$\frac{d y}{d x}= e ^{ x + y }+ x ^2 e ^{ y }$

→
$\int[\operatorname{cosec}(\log x)][1-\cot (\log x)] d x$
→
If $\vec{\text{a}}=\hat{\text{i}}+\hat{\text{j}},\ \vec{\text{b}}=\hat{\text{j}}+\hat{\text{k}},\ \vec{\text{c}}=\hat{\text{k}}+\hat{\text{i}}$, find the unit vector in the direction of $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}$.
→
The function $f(x)=x^3-3 x^2+3 x-100, x \in R$ is $.......$
→
Write the value of $\tan\Big(2\tan^{-1}\frac{1}{5}\Big)$
→
If $A=\{2,3,4,5,6\}$, then which of the following is 'not' true ?
→
Find $\frac{\text{dy}}{\text{dx}},$ when
$\text{x}=\text{b}\sin^2\theta\text{ and y}=\text{a}\cos^2\theta$
→
Diffrentiate the following w.r.t.x

$e^{\log [(\log x) 2-\log x 2]}$

→
Write the value of $\begin{vmatrix}\text{a}+\text{ib}&\text{c}+\text{id}\\-\text{c}+\text{id}&\text{a}-\text{ib}\end{vmatrix}$
→
If $\vec{\text{a}}=\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}},\ \vec{\text{b}}=2\hat{\text{i}}-\hat{\text{j}}+3\hat{\text{k}}$and $\vec{\text{c}}=\hat{\text{i}}-2\hat{\text{j}}+\hat{\text{k}}$, find a unit vector parallel to $2\vec{\text{a}}-\vec{\text{b}}+3\vec{\text{c}}$.
→