Download App

Scalar Or Dot Product — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsScalar Or Dot Product3 Marks
Question
Write the projection of $\vec{\text{b}}+\vec{\text{c}}$ on $\vec{\text{a}}$ when $\vec{\text{a}}=2\hat{\text{i}}-2\hat{\text{j}}+\hat{\text{k}},\vec{\text{b}}=\hat{\text{i}}+2\hat{\text{j}}-2\hat{\text{k}}$ and $\vec{\text{c}}=2\hat{\text{i}}-\hat{\text{j}}+4\hat{\text{k}}.$
✓

Answer

Given that
$\vec{\text{a}}=2\hat{\text{i}}-2\hat{\text{j}}+\hat{\text{k}}$
$\vec{\text{b}}=\hat{\text{i}}+2\hat{\text{j}}-2\hat{\text{k}}$
$\vec{\text{c}}=2\hat{\text{i}}-\hat{\text{j}}+4\hat{\text{k}}$
$\vec{\text{b}}+\vec{\text{c}}=\hat{\text{i}}+2\hat{\text{j}}-2\hat{\text{k}}+2\hat{\text{i}}-\hat{\text{j}}+4\hat{\text{k}}$
$=3\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}}$
Projection of $\vec{\text{b}}+\vec{\text{c}}$ on $\vec{\text{a}}$ is
$\frac{\big(\vec{\text{b}}+\vec{\text{c}}\big).\vec{\text{a}}}{|\vec{\text{a}}|}$
$=\frac{\big(3\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}}\big).\big(2\hat{\text{i}}-2\hat{\text{j}}+\hat{\text{k}}\big)}{2\hat{\text{i}}-2\hat{\text{j}}+\hat{\text{k}}}$
$=\frac{6-2+2}{\sqrt{4+4+1}}$
$=\frac{6}{3}$
$=2$

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

Evaluate the following integrals:
$\int\frac{\sin(2+3\log\text{x})}{\text{x}}\text{ dx}$
→
Diffrentiate the following w.r.t.x

$\cot \left(\frac{\log x}{2}\right)-\log \left(\frac{\cot x}{2}\right)$

→
Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards. Find the mean, variance and standard deviation of the number of kings drawn.
→
Find the shortest distance between the lines $\bar{r}=(4 \hat{i}-\hat{j})+\lambda(\hat{i}+2 \hat{j}-3 \widehat{k})$ and $\bar{r}=(\hat{i}-\hat{j}-2 \widehat{k})+\mu(\hat{i}+4 \hat{j}-5 \widehat{k})$
→
The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that (i) all 8 machines (ii) 7 or 8 machines (iii) at most 6 machines will produce all bolts within specification.
→
Write the value of b which $\text{f(x)}=\begin{cases}5\text{x}-4,&0<\text{x}\leq1\\4\text{x}^2+3\text{bx},&1<\text{x}<2\end{cases}$ is continuous at x = 1.
→
Two cards are drawn successively with replacement from well shuffled pack of 52 cards. Find the probability distribution of the number of aces.
→
Diffrentiate the following w. r. t. x.

$\cot ^{-1}\left(\frac{1+35 x^2}{2 x}\right)$

→
Evaluate the following:

$\int_1^{\infty} \frac{1}{\sqrt{x}(1+x)} d x$

→
Find the angle between two lines, one of which has direction ratios 2, 2, 1 while the other one is obtained by joining the points (3, 1, 4) and (7, 2, 12).
→