Download App

Algebra of Vectors — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Vectors2 Marks
Question
If $\vec{\text{a}}=\text{x}\hat{\text{i}}+2\hat{\text{j}}-\text{z}\hat{\text{k}}$ and $\vec{\text{b}}=3\hat{\text{i}}-\text{y}\hat{\text{j}}+\hat{\text{k}}$ are two equal vectors, then write the value of x + y + z.
✓

Answer

Given: $\vec{\text{a}}=\text{x}\hat{\text{i}}+2\hat{\text{j}}-\text{z}\hat{\text{k}}$ and $\vec{\text{b}}=3\hat{\text{i}}-\text{y}\hat{\text{j}}+\hat{\text{k}}$ Since the two vectors are equal. We have,$\vec{\text{a}}=\text{x}\hat{\text{i}}+2\hat{\text{j}}-\text{z}\hat{\text{k}}=\vec{\text{b}}=3\hat{\text{i}}-\text{y}\hat{\text{j}}+\hat{\text{k}}$
$\Rightarrow\ \text{x}=3,\ \text{y}=-2,\ \text{z}=-1$
$\therefore\ \text{x + y + z}=3-2-1=0$

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 "Solve the Following Question.(2 Marks)" from Algebra of Vectors→Algebra of Vectors — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Evaluate the following integrals:
$\int\sqrt{1+\text{e}^\text{x}}\text{ e}^\text{x}\text{dx}$
→
If $\text{A}=\begin{bmatrix}5&3&8\\2&0&1\\1&2&3\end{bmatrix}.$ Write the cofactor of element $a_{32}$​​​​​​​.
→
Find the measure of the acute angle between the line represented by $3 x^2-4 \sqrt{3} x y+3 y^2=0$
→
If $\begin{bmatrix}2\text{x+y}&3\text{y}\\0&4 \end{bmatrix}=\begin{bmatrix}6&0\\6&4\end{bmatrix}$, then find x.
→
Evaluate: $\int \frac{1}{\sin x \cdot \cos ^2 x} d x$
→
Evaluate $\int\frac{\cos\sqrt{\text{x}}}{\sqrt{\text{x}}}\text{ dx}$
→
The probability distribution of $X$ is as follows:
$X=x$ $0$ $1$ $2$ $3$ $4$
$P(X=x)$ $0.1$ $K$ $2K$ $2K$ $K$
Find $(i) \ K$ $(ii) \ P(X < 2)$
→
Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency. [(p → q) ∧ q)] → p
→
Find the principal solutions of the following equations :

$\cos \theta=\frac{1}{2}$

→
Write necessary condition for a point x = c to be an extreme point of the function f(x).
→