If the vectors 3i+ ,j+k and 2i-j+8k are perpendicular, then is - Vidyadip

MCQ

If the vectors $3i+\lambda \,j+k$ and $2i-j+8k$ are perpendicular, then $\lambda $ is

A
$-14$
B
$7$
✓
$14$
D
$1/7$

✓

Answer

Correct option: C.

$14$

c
(c) Let $a = 3i + \lambda \,j + k$,$b = 2i - j + 8k$

$\because a \bot \,b$ $\therefore a\,.\,b = 0$

$(3i + \lambda \,j + k)\,.\,(2i - j + 8k) = 0$

$a,\,b,\,c$ $ \Rightarrow \lambda = 14.$

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 10. vector algebra→10. 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

The sides of an equilateral triangle are increasing at the rate of 2cm/ sec. The rate at which the area increases, when side is 10cm is:

Two persons A and B take turns in throwing a pair of dice.The first person to throw 9 from both dice will be awarded the prize. If A throws first, then the probability that B wins the game is.

$\frac{9}{17}$
$\frac{8}{17}$
$\frac{8}{9}$
$\frac{1}{9}$

If $A$ is a square matrix and $A^2=A$, then $(I+A)^2-3 A$ is equal to

$\Bigg(\cot\Bigg(\sin^{-1}\sqrt{\frac{2-\sqrt{3}}{4}}+\cos^{-1}\frac{\sqrt{-12}}{4}+\sec^{\sqrt{2}}\Bigg)\Bigg)$ is:

0
$ 2π$
$ 3π$
none of these

Consider a function $f:R \to R$

$f\left( {x + a} \right) = \frac{1}{2} + \sqrt {f\left( x \right) - {f^2}\left( x \right)}$ a is a real constant, then $f(x)$ must be

Consider a function $f:\left[ { - 1,1} \right] \to R$ where $f(x) = {\alpha _1}{\sin ^{ - 1}}x + {\alpha _3}\left( {{{\sin }^{ - 1}}{x^3}} \right) + ..... + {\alpha _{(2n + 1)}}{({\sin ^{ - 1}}x)^{(2n + 1)}} - {\cot ^{ - 1}}x$ Where $\alpha _i\ 's$ are positive constants and $n \in N < 100$ , then $f(x)$ is

Let $f : [1, 3] \to R$ be a function satisfying $\frac{x}{{[x]}} \le f(x) \le \sqrt {6 - x} ,$ for all $x \ne 2$ and $f(2) = 1,$ where $R$ is the set of all real numbers and $[x]$ denotes the largest integer less than or equal to $x.$

Statement $1:$ $\mathop {\lim }\limits_{x \to {2^ - }} \,f(x)$ exists.

Statement $2:$ $f$ is continuous at $x = 2.$

If the direction ratios of a line are $1, - 3,\,2$, then the direction cosines of the line are

$f (x) =$ $\frac{x}{{\ln x}}\,$ and $g (x) =$ $\frac{{\ln x}}{x}\,$. Then identify the $CORRECT $ statement

If ${\sin ^{ - 1}}a + {\sin ^{ - 1}}b + {\sin ^{ - 1}}c = \pi ,$ then the value of $a\sqrt {(1 - {a^2})} + b\sqrt {(1 - {b^2})} + c\sqrt {(1 - {c^2})} $ will be