If a = x i + 2 j - z k and = b = 3 i - y j + k are two equal vect… - Vidyadip

Question

If $\overrightarrow{\text{a}} = \text{x}\hat{\text{i}} + 2 \hat{\text{j}} - \text{z}\hat{\text{k}}\text{ and } = \overrightarrow{\text{b}} = 3\hat{\text{i}} - \text{y}\hat{\text{j}} + \hat{\text{k}}$ are two equal vectors, then write the value of x + y + z.

✓

Answer

$\because\overrightarrow{\text{a}} = \overrightarrow{\text{b}}$
$\text{x}\hat{\text{i}} + 2\hat{\text{j}} - \text{z}\hat{\text{k}} = 3\hat{\text{i}} - \text{y}\hat{\text{j}} + \hat{\text{k}}$
Equating, we get, x = 3,
$ -\text{y} = 2 \Rightarrow\text{y} = - 2$
$ - \text{z} = 1 \Rightarrow\text{z} = -1$
$\therefore\text{x} + \text{y} +\text{z} = 3-2-1 = 0 .$

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 "1 Marks Question" 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

$\text{If}\ \sin^{-1}\text{x = y},$ then

If $x+y=\left[\begin{array}{ll}2 & 1 \\ 1 & 2\end{array}\right]$ and $2 x-y=\left[\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right]$ then find the value of $x$.

Examine the following functions for continuity.
f(x) = x - 5

Integrate the function sin mx w.r.t. x.

Evaluate the following:
$\text{cosec}^{-1}\Big(\text{cosec}\frac{\pi}{4}\Big)$

Let A be the set of all 50 students of Class X in a school. Let f : $A \rightarrow N$ be function defined by f(x) = roll number of the student x. Show that f is one-one but not onto.

Evaluate the following:
$\sin^{-1}\Big(\sin\frac{\pi}{6}\Big)$

The Integrating Factor of the differential equation $\left(1-y^{2}\right) \frac{d x}{d y}+y x=a y~(-1<y<1)$ is

Integrate the function $e^{2x}$ sin $x$

Write the degree of the differrntial equation $\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}+3\Big(\frac{\text{dy}}{\text{dx}}\Big)^{2}=\text{x}^{2}\log\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}\Big).$