Download App

Scalar Or Dot Product — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsScalar Or Dot Product3 Marks
Question
Dot product of a vector with vectore $\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}},2\hat{\text{i}}+\hat{\text{j}}-3\hat{\text{k}}$ and $\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ are respectively 4, 0 and 2. Find the vector.
✓

Answer

Let $\text{a}\hat{\text{i}}+\text{b}\hat{\text{j}}+\text{c}\hat{\text{k}}$ be the required vector.
Given that
$\big(\text{a}\hat{\text{i}}+\text{b}\hat{\text{j}}+\text{c}\hat{\text{k}}\big).\big(\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}\big)=4$
$\Rightarrow\text{a}-\text{b+c}=4\dots(1)$
$\big(\text{a}\hat{\text{i}}+\text{b}\hat{\text{j}}+\text{c}\hat{\text{k}}\big).\big(2\hat{\text{i}}+\hat{\text{j}}-3\hat{\text{k}}\big)=0$
$\Rightarrow2\text{a}+\text{b}-3\text{c}=0\dots(2)$
$\big(\text{a}\hat{\text{i}}+\text{b}\hat{\text{j}}+\text{c}\hat{\text{k}}\big).\big(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}\big)=2$
$\Rightarrow\text{a+b}+\text{c}=2\dots(3)$
Solving (1), (2) and (3), we get
$\text{a}=2,\text{b}=-1,\text{c}=1$
So, $\text{a}\hat{\text{i}}+\text{b}\hat{\text{j}}+\text{c}\hat{\text{k}}=2\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$

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.(3 Marks)" from Scalar Or Dot Product→Scalar Or Dot Product — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

In $\triangle A B C$ prove that $\sin \frac{A}{2} \cdot \sin \frac{A}{2} \cdot \sin \frac{A}{2}=\frac{[A(\triangle A B C)]^2}{a b c s}$
→
Find the principal value of the following:
$\sec^{-1}\Big(-\sqrt2\Big)$
→
Find the area of the triangle with vertices (1, 1, 0), (1, 0, 1) and (0, 1, 1).
→
In $\triangle ABC$, prove that $\sin \left(\frac{ A - B }{2}\right)=\left(\frac{ a - b }{ c }\right) \cos \left(\frac{ C }{2}\right)$
→
Classify the following functions as injection, surjection or bijection:
$f : R \rightarrow R,$ defined by $f(x) = \sin x$
→
The total cost $C(x)$ associated with the production of $x$ units of an item is given by $C(x)=0.007 x^3-0.003 x^2+15 x+4000$. Find the marginal cost when 17 units are produced.
→
Evaluate the following integrals:$\int\text{e}^{\text{x}}\big[\sec\text{x}+\log(\sec\text{x}+\tan\text{x})\big]\text{dx}$
→
If $\text{A}=\begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}\text{ and A (adj A =)}\begin{bmatrix} \text{k} & 0 \\ 0 & \text{k} \end{bmatrix},$ then find the value of k.
→
Evaluate : $\int_1^2 \frac{\log x}{x^2} \cdot d x$
→
If A = {1, 2, 3}, show that a one-one function f : A → A must be onto.
→