Download App

VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA1 Mark
Question
State True or False for the following:
If $|\vec{\text{a}}+\vec{\text{b}}|=|\vec{\text{a}}-\vec{\text{b}}|,$ then the vector $\vec{\text{a}}$ and $\vec{\text{b}}$ are orthogonal.
✓

Answer

True.Solution:
Given, $|\vec{\text{a}}+\vec{\text{b}}|=|\vec{\text{a}}-\vec{\text{b}}|$
$\Rightarrow|\vec{\text{a}}+\vec{\text{b}}|^2=|\vec{\text{a}}-\vec{\text{b}}|^2$
$\Rightarrow|\vec{\text{a}}|^2+|\vec{\text{b}}|^2+2\vec{\text{a}}\cdot\vec{\text{b}}=|\vec{\text{a}}|^2+|\vec{\text{b}}|^2-2\vec{\text{a}}\cdot\vec{\text{b}}$
$\Rightarrow2\vec{\text{a}}\cdot\vec{\text{b}}=-2\vec{\text{a}}\cdot\vec{\text{b}}$
$\Rightarrow4\vec{\text{a}}\cdot\vec{\text{b}}=0$
$\Rightarrow\vec{\text{a}}\cdot\vec{\text{b}}=0$
Hence, $\vec{\text{a}}$ and $\vec{\text{b}}$ are orthogonal.

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 "True False[1 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

State True or False for the statements:
Rolle’s theorem is applicable for the function f(x) = |x - 1| in [0, 2].
→
State True or False for the following:
If $\vec{\text{a}}$ and $\vec{\text{b}}$ are adjacent sides of a rhombus, then $\vec{\text{a}}\cdot{\text{b}}=0.$
→
State True or False for the following:
If the foot of perpendicular drawn from the origin to a plane is (5, -3, -2), then the equation of plane is $\vec{\text{r}}\cdot(5\hat{\text{i}}-3\hat{\text{j}}-2\hat{\text{k}})=38.$
→
State True or False for the following:
The solution of $\frac{\text{dy}}{\text{dx}}=\Big(\frac{\text{y}}{\text{x}}\Big)^{\frac{1}{3}}$ is $\text{y}^{\frac{2}{3}}-\text{x}^{\frac{2}{3}}=\text{C}.$
→
Which of the following statements are True or False.
If A is skew symmetric matrix, then $A^2$ is a symmetric matrix.
→
State True or False for the following:
The vector equation of the line $\frac{\text{x}-5}{3}=\frac{\text{y}-4}{7}=\frac{\text{z}-6}{2}$ is $\vec{\text{r}}=5\hat{\text{i}}-4\hat{\text{j}}+6\hat{\text{k}}+\lambda(3\hat{\text{i}}-7\hat{\text{j}}+2\hat{\text{k}}).$
→
Which of the following statements are True or False.
Matrix multiplication is commutative.
→
Which of the following statements are True or False.
Matrices of different order can not be subtracted.
→
State True or False for the statements of the following Exercise:
$\big(\text{A}^3\big)^{-1}=(\text{A}^{-1})^3,$ where A is square matrx and |A| ≠ 0.
→
State whether the statements are True or False:
In a LPP, the maximum value of the objective function Z = ax + by is always finite.
→