Download App

VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA3 Marks
Question
If $|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=5$ and $\big|\vec{\text{a}}\times\vec{\text{b}}\big|=8,$ find $\vec{\text{a}}.\vec{\text{b}}.$
✓

Answer

We know
$\big(\vec{\text{a}}.\vec{\text{b}}\big)^2+\big|\vec{\text{a}}\times\vec{\text{b}}\big|^2=|\vec{\text{a}}|^2\big|\vec{\text{b}}\big|^2$
$\Rightarrow\big(\vec{\text{a}}.\vec{\text{b}}\big)^2+8^2=2^2\times5^2$ $\big(\therefore\big|\vec{\text{a}}\times\vec{\text{b}}\big|=8,|\vec{\text{a}}|=2$and $\big|\vec{\text{b}}\big|=5\big)$
$\Rightarrow\big(\vec{\text{a}}.\vec{\text{b}}\big)^2+64=100$
$\Rightarrow\big(\vec{\text{a}}.\vec{\text{b}}\big)^2=36$
$\Rightarrow\big(\vec{\text{a}}.\vec{\text{b}}\big)=6$

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 "3 Marks" 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

Find fog and gof if:

f(x) = x2 + 2, $\text{g(x)}=1-\frac{1}{1-\text{x}}$

→
Find the value of $\lambda$ so that the following vectors are coplanar:
$\vec{\text{a}}=2\hat{\text{i}}-\hat{\text{j}}++\hat{\text{k}},\vec{\text{b}}=\hat{\text{i}}+2\hat{\text{j}}-3\hat{\text{k}},\vec{\text{c}}=\lambda\hat{\text{i}}+\lambda\hat{\text{j}}+5\hat{\text{k}}$
→
Evaluate the following integrals:
$\int^\limits4_{-4}|\text{x}+2|\text{dx}$
→
Classify the following functions as injection, surjection or bijection:
f : R → R, defined by f(x) = x3 + 1
→
Prove the following results:
$\sin^{-1}\frac{4}{5}+2\tan^{-1}\frac{1}{3}=\frac{\pi}{2}$
→
Find $\Big[\vec{\text{a}}\ \vec{\text{b}}\ \vec{\text{c}}\Big]$, when
$\vec{\text{a}}=\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}},\vec{\text{b}}=2\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}}$ and $\vec{\text{c}}=\hat{\text{j}}+\hat{\text{k}}$
→
Evaluate the following:
$\tan\frac{1}{2}\Big(\cos^{-1}\frac{\sqrt5}{3}\Big)$
→
Show that $\frac{\text{logx}}{\text{x}}$ has a minimum value at x = e.
→
$\int \text{(2x} - 3)^{5} + \sqrt{3\text{x + 2}}\text{ dx}$
→
Test whether the following relations R1 are:
  1. Reflexive.
  2. Symmetric.
  3. Transitive.
R1 on Q0 defined by $(\text{a, b})\in\text{R}_1\Leftrightarrow\ \text{a}=\frac{1}{\text{b}}.$
→