If |a| , = 3, , ,|b| , = 4 then a value of for which a + b is per… - Vidyadip

MCQ

If $|a|\, = 3,\,\,|b|\, = 4$ then a value of $\lambda$ for which $a + \lambda b$ is perpendicular to $a - \lambda b$ is

A
$\frac{9}{16}$
✓
$\frac{3}{4}$
C
$\frac{3}{2}$
D
$\frac{4}{3}$

✓

Answer

Correct option: B.

$\frac{3}{4}$

b
(b) Since $a + \lambda b$ is perpendicular to $a - \lambda b$, then their product will be zero.

So, $(a + \lambda b).(a - \lambda b) = 0$ ==> $|a{|^2} - {\lambda ^2}|b{|^2} = 0$

or ${\lambda ^2} = \frac{{|a{|^2}}}{{|b{|^2}}} \Rightarrow {\lambda ^2} = \frac{9}{{16}}$ or $\lambda = \pm \frac{3}{4}$,

$[\because \,|a| = 3,|b| = 4]$

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 STD 12 - 10. vector algebra→STD 12 - 10. vector algebra — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The area bounded by the lines $y = |x – 2|, x = 1, x = 3$ and the $x-$ axis is:

The differential equation of all ‘Simple Harmonic Motions’ of given period $\frac{2\pi}{\text{n}}$ is:

Let $f: R \rightarrow R$ be given by $f(x)=x^2-3$. Then, $f^{-1}$ is given by:

Let $\quad \overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}+\alpha \hat{\mathrm{j}}+\hat{\mathrm{k}}, \quad \overrightarrow{\mathrm{b}}=-\hat{\mathrm{i}}+\hat{\mathrm{k}}, \quad \overrightarrow{\mathrm{c}}=\beta \hat{\mathrm{j}}-\hat{\mathrm{k}}$, where $\alpha$ and $\beta$ are integers and $\alpha \beta=-6$. Let the values of the ordered pair $(\alpha, \beta)$ for which the area of the parallelogram of diagonals $\vec{a}+\vec{b}$ and $\vec{b}+\vec{c}$ is $\frac{\sqrt{21}}{2}$, be $\left(\alpha_1, \beta_1\right)$ and $\left(\alpha_2, \beta_2\right)$. Then $\alpha_1^2+\beta_1^2-\alpha_2 \beta_2$ is equal to

Let G be the centroid of $\triangle{\text{ABC}}$. if $\overrightarrow{\text{AB}}=\vec{\text{a}},\overrightarrow{\text{AC}}=\vec{\text{b}}$, then the bisector $\overrightarrow{\text{AG}}$, in terms of $\vec{\text{a}}$ and $\vec{\text{b}}$ is,

If $\text{A} = \begin{bmatrix}1\end{bmatrix}$ then the order of the matrix is:

The solution of the equation $\frac{{dy}}{{dx}} = \frac{{x + y}}{{x - y}}$ is

Find the values of $x,$ if: $\begin{vmatrix} 2 &\text{amp; } 4 \\ 5 &\text{amp; } 1 \end{vmatrix}= \begin{vmatrix} 2\text{x} &\text{amp; }4 \\ 6 &\text{amp; x} \end{vmatrix}$

Choose the correct answer from the given four option.
The number of solutions of $\frac{\text{d}\text{y}}{\text{d}\text{x}}=\frac{\text{y+1}}{\text{x}-1}$ when y(1) = 2:

The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{x^2 \cos x}{1+e^x} d x$ is equal to