Download App

Vector Algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVector Algebra1 Mark
MCQ
Choose the correct answer from the given four options. Find the value of $\lambda$ such that the vectors $\vec{\text{a}}=2\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{a}}=\hat{\text{i}}+2\hat{\text{j}}+3\hat{\text{k}}$ are orthogonal:
  • A
    $0$
  • B
    $1$
  • C
    $\frac{3}{2}$
  • ✓
    $-\frac{5}{2}$
✓

Answer

Correct option: D.
$-\frac{5}{2}$
Given two non$-$zero vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ are orthogonal
$\therefore\ \vec{\text{a}}\cdot\vec{\text{b}}=0$
$\therefore\ (2\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}})\cdot(\hat{\text{i}}+2\hat{\text{j}}+\hat{3\text{k}})=0$
$\Rightarrow2+2\lambda+3=0$
$\Rightarrow\lambda=-\frac{5}{2}$

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 "M.C.Q (1 Marks)" from Vector Algebra→Vector Algebra — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If the system of linear equations  $2 x + y - z =7$ ; $x-3 y+2 z=1$  ; $x +4 y +\delta z = k$, where $\delta, k \in R$  has infinitely many solutions, then $\delta+ k$ is equal to
→
The order and degree of the differential equation $\Big(1+3\frac{\text{dy}}{\text{dx}}\Big)^\frac{2}{3}=4\frac{\text{d}^3\text{y}}{\text{dx}^3}$ are:
→
If $B$ is a non$-$singular matrix and $A$ is a square matrix, then $\text{det} (B^{-1} AB)$ is equal to:
→
If $f(x)$ = $\int\limits_0^x {2\,({{\cos }^{2\,}}\,3t\, + \,3\,{{\sin }^{2\,}}\,3t)dt} $ , then $f ( x + \pi )$ is eual to
→
$\int(\text{x}-1)\text{e}^{-\text{x}}\text{ dx}$ is equal to:
→
Find the value of $:\ \sec^2 (\tan^{-1} 2) +\csc^2 (\cot^{-1} 3)$
→
The value of integral $\int\limits_{\frac{\pi }{4}}^{\frac{{3\pi }}{4}} {\frac{x}{{1 + \sin x}}} dx$ is
→
Five fair coins are tossed simultaneously. The probability of the events that atleast one head comes up is
→
If $A = \left[ {\begin{array}{*{20}{c}}2&0&0\\0&2&0\\0&0&2\end{array}} \right],$then ${A^5} = $
→
The interval in which the function ${x^3} $ increases less rapidly than $6{x^2} + 15x + 5$, is
→