Download App

VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA5 Marks
Question
Let $\vec{\text{u}},\vec{\text{v}}$ and $\vec{\text{w}}$ be vectors such $\vec{\text{u}}+\vec{\text{v}}+\vec{\text{w}}=\vec{0}.$ If $|\vec{\text{u}}|=3,|\vec{\text{v}}|=4$ and $|\vec{\text{w}}|=5,$ then find $\vec{\text{u}}.\vec{\text{v}}+\vec{\text{v}}.\vec{\text{w}}+\vec{\text{w}}.\vec{\text{u}}.$
✓

Answer

Here, $\vec{\text{u}}+\vec{\text{v}}+\vec{\text{w}}=0$
Squaring both the sides,
$\big(\vec{\text{u}}+\vec{\text{v}}+\vec{\text{w}}\big)^2=(0)^2$
$|\vec{\text{u}}|^2+|\vec{\text{v}}|^2+|\vec{\text{w}}|^2+2\vec{\text{u}}\vec{\text{v}}+2\vec{\text{v}}\vec{\text{w}}+2\vec{\text{w}}\vec{\text{u}}=0$
$(3)^2+(4)^2+(5)^2+2\big(\vec{\text{u}}.\vec{\text{v}}+\vec{\text{v}}.\vec{\text{w}}+\vec{\text{w}}.\vec{\text{u}}\big)=0$
$9+16+25+2\big(\vec{\text{u}}\vec{\text{v}}+\vec{\text{v}}\vec{\text{w}}+\vec{\text{w}}\vec{\text{u}}\big)=0$
$2\big(\vec{\text{u}}\vec{\text{v}}+\vec{\text{v}}\vec{\text{w}}+\vec{\text{w}}\vec{\text{u}}\big)=-50$
$\vec{\text{u}}\vec{\text{v}}+\vec{\text{v}}\vec{\text{w}}+\vec{\text{w}}\vec{\text{u}}=\frac{-50}{2}$
$\vec{\text{u}}\vec{\text{v}}+\vec{\text{v}}\vec{\text{w}}+\vec{\text{w}}\vec{\text{u}}=-25$

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 "5 Marks Questions" 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

If $\text{A} = \begin{bmatrix}2&-3&5\\3&2&-4\\1&1&-2\end{bmatrix},$ find $A^{-1}.$ Using $A^{-1}$ solve the system of equations:
$2x - 3y + 5z = 11$
$3x + 2y - 4z = -5$
$x + y - 2z = -3$
→
Solve the following differential equations:$\text{y}(1+\text{e}^{\text{x}})\text{dy}=(\text{y}+1)\text{e}^{\text{x}}\text{ dx}$
→
Evaluate the following integrals:$\int\frac{1}{\cos\text{x}+\text{cosec x}}\text{dx}$
→
Solve the following systems of homogeneous linear equations by matrix method:
$x + y + z = 0$
$x - y - 5z = 0$
$x + 2y + 4z = 0$
→
Differentiate $\tan^{-1} \bigg(\frac{\sqrt{1 + x^{2} - 1}}{x}\bigg)$ w.r.t. $\sin^{-1} \frac{2x}{1 + x^{2}}, \text{ if } x \in (-1, 1)$
→
The standard weight of a special purpose brick is 5 kg and it must contain two basic ingredients $\text{B}_{1} \text{and} \text{B}_{2}. \text{B}_{1}$ costs ₹ 5 per kg and $\text{B}_{2}$ costs ₹ 8 per kg. Strength considerations dictate that the brick should contain not more than 4 kg of $\text{B}_{1}$ and minimum 2 kg of $\text{B}_{2}$. Since the demand for the product is likely to be related to the price of the brick, find the minimum cost of brick satisfying the above conditions. Formulate this situation as an LPP and solve it graphically.
→
If A and B are two events such that $2\text{P(A)}=\text{P(B)}=\frac{5}{13}$ and $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\frac{2}{5}$ find $\text{P}(\text{A}\cap\text{B}).$
→
Differentiate the following functions with respect to x:
$(\text{x}^\text{x})\sqrt{\text{x}}$
→
Evaluate: $\int\frac{\text{cos 2x}\text{ - cos }\alpha}{\text{cos x - cos }\alpha}\text{dx}.$
→
Using differentials, find the approximate values of the following:
$\cos61^\circ$ it being given that $\sin60^\circ=0.86603$ and $0.01745$ radian
→