Download App

Vectors — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsVectors2 Marks
Question
Show that, for any vectors $\bar{a}, \bar{b}, \bar{c}$

$(\bar{a}+\bar{b}+\bar{c}) \times \bar{c}+(\bar{a}+\bar{b}+\bar{c}) \times \bar{b}+(\bar{b}+\bar{c}) \times \bar{a}=2 \bar{a} \times \bar{c}$

Question is modified.

For any vectors $\bar{a}, \bar{b}, \bar{c}$ show that

$(\bar{a}+\bar{b}+\bar{c}) \times \bar{c}+(\bar{a}+\bar{b}+\bar{c}) \times \bar{b}+(\bar{b}-\bar{c}) \times \bar{a}$

$=2 \bar{a} \times \bar{c}$.

✓

Answer

$\begin{aligned} & \text { LHS }=(\bar{a}+\bar{b}+\bar{c}) \times \bar{c}+(\bar{a}+\bar{b}+\bar{c}) \times \bar{b}+(\bar{b}-\bar{c}) \times \bar{a} \\ & =\bar{a} \times \bar{c}+\bar{b} \times \bar{c}+\bar{c} \times \bar{c}+\bar{a} \times \bar{b}+\bar{b} \times \bar{b}+\bar{c} \times \bar{b}+\bar{b} \times \bar{a}-\bar{c} \times \bar{a} \\ & =\bar{a} \times \bar{c}+\bar{b} \times \bar{c}+\overline{0}+\bar{a} \times \bar{b}+\overline{0}-\bar{b} \times \bar{c}-\bar{a} \times \bar{b}+\bar{a} \times \bar{c}\end{aligned}$

$\ldots[\because \bar{a} \times \bar{b}=-\bar{b} \times \bar{a}]$

$=2 \bar{a} \times \bar{c}=\mathrm{RHS}$

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 Vectors→Vectors — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Integrate the following functions w.r.t. x:

$\sqrt{4^x\left(4^x+4\right)}$

→
Find the vector equation of the plane which is at a distance of 6 unit from the origin and to which the vector $2 \hat{i}-\hat{j}+2 \hat{k}$ is normal.
→
Find the area of the parallelogram whose adjacent sides are the vectors $\bar{a}=2 \hat{i}-2 \hat{j}+\hat{k}$

and $\bar{b}=\hat{i}-3 \hat{j}-3 \hat{k}$.

→
Differentiate $\sin^2 (\sin^{−1}(x^2))$ w.r. to $x$
→
$A$ matrix $A$ of order $3 \times 3$ has determinant $5$. What is the value of $|3A|$?
→
A, B, C are three non-null square matrices of the same order, write the condition on A such that AB = AC ⇒ B = C.
→
For any three vectors $\vec{\text{a}},\vec{\text{b}}$ and $\vec{\text{c}}$ write the value of $\vec{\text{a}}\times\big(\vec{\text{b}}+\vec{\text{c}}\big)+\vec{\text{b}}\times\big(\vec{\text{c}}+\vec{\text{a}}\big)+\vec{\text{c}}\times\big(\vec{\text{a}}+\vec{\text{b}}\big).$
→
Write the equation of the plane passing through (2, −1, 1) and parallel to the plane 3x + 2y − z = 7.
→
Diffrentiate the following w.r.t.x

$\sin \sqrt{\sin \sqrt{x}}$

→
A random variable $X \sim N(0,1)$. Find $P(X>0)$ and $P(X<0)$
→