Download App

Vector or Cross Product — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsVector or Cross Product3 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 "Solve the Following Question.(3 Marks)" from Vector or Cross Product→Vector or Cross Product — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the direction cosines and direction angles of the vector.

$(1 / 2) \hat{i}+\hat{j}+\hat{k}$

→
Write a value of $\int\frac{1}{1+2\text{e}^{\text{x}}}\text{dx}$
→
Write the value of $\tan^{-1}\frac{\text{a}}{\text{b}}-\tan^{-1}\Big(\frac{\text{a}-\text{b}}{\text{a}+\text{b}}\Big).$
→
Find the joint equation of the pair of lines through the origin each of which is making an angle of $30^{\circ}$ with the line
$3 x+2 y-11=0$
→
Check the commutativity and associativity of the following binary operations:
'*' on Q defined by a * b = a + ab for all a, b ∈ Q.
→
Find the value of $\lambda$ so that the following lines are perpendicular to each other.$\frac{\text{x}-5}{5\lambda+2}=\frac{2-\text{y}}{5}=\frac{1-\text{z}}{-1},\frac{\text{x}}{1}=\frac{2\text{y}+1}{4\lambda}=\frac{1-\text{z}}{-3}$
→
Solve the differential equation : $\frac{d y}{d x}=\frac{y+\sqrt{x^2+y^2}}{x}$
→
Find the general solutions of the following : cos 4θ = cos 2θ
→
Evaluate the following integrals:
$\int3\sqrt{\cos^2\text{x}}\sin\text{x }\text{dx}$
→
Let $\vec{\text{a}}=5\hat{\text{i}}-\hat{\text{j}}+7\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}-\hat{\text{j}}+\lambda\hat{\text{k}}.$ Find $\lambda$ such that $\vec{\text{a}}+\vec{\text{b}}$ is orthonal to $\vec{\text{a}}-\vec{\text{b}}.$
→