A vector which bisects the angle between a = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given vectors are $a = 3 \hat{i} - 4 \hat{k}$ and $b = 5 \hat{j} + 12 \hat{k}$.The magnitudes of the vectors are:$|a| = \sqrt{3^2 + (-4)^2} = \sqr

Vedclass · Accepted Answer

$39 \hat{i} + 25 \hat{j} + 8 \hat{k}$

Vedclass · Answer

(B) Given vectors are $a = 3 \hat{i} - 4 \hat{k}$ and $b = 5 \hat{j} + 12 \hat{k}$.The magnitudes of the vectors are:$|a| = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5$$|b| = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13$The unit vectors along $a$ and $b$ are $\hat{a} = \frac{a}{|a|} = \frac{3 \hat{i} - 4 \hat{k}}{5}$ and $\hat{b} = \frac{b}{|b|} = \frac{5 \hat{j} + 12 \hat{k}}{13}$.$A$ vector that bisects the angle between $a$ and $b$ is given by the sum of the unit vectors: $\hat{a} + \hat{b}$.$\hat{a} + \hat{b} = \frac{3 \hat{i} - 4 \hat{k}}{5} + \frac{5 \hat{j} + 12 \hat{k}}{13}$Taking the common denominator $65$:$= \frac{13(3 \hat{i} - 4 \hat{k}) + 5(5 \hat{j} + 12 \hat{k})}{65}$$= \frac{39 \hat{i} - 52 \hat{k} + 25 \hat{j} + 60 \hat{k}}{65}$$= \frac{39 \hat{i} + 25 \hat{j} + 8 \hat{k}}{65}$Since any scalar multiple of this vector also bisects the angle,we can multiply by $65$ to get the vector $39 \hat{i} + 25 \hat{j} + 8 \hat{k}$.

$A$ vector which bisects the angle between $a = 3 \hat{i} - 4 \hat{k}$ and $b = 5 \hat{j} + 12 \hat{k}$ is

Similar Questions

Given vectors $\vec{a} = 2 \hat{i} - \hat{j} + 2 \hat{k}$ and $\vec{b} = -\hat{i} + \hat{j} - \hat{k}$. The vector in the direction of $\vec{a} + \vec{b}$ with magnitude $\sqrt{2}$ is . . . . . . .

In $\triangle OAC$,if $B$ is the mid-point of side $AC$ and $\vec{OA}=\vec{a}, \vec{OB}=\vec{b}$,then $\vec{OC}$ is equal to

The unit vector in the direction of the vector $(1, 0, 0)$ is $.......$

In the given figure (a square),identify the co-initial vectors.

Represent graphically a displacement of $40 \, km,$ $30^\circ$ west of south.

Vedclass Test Series

Exam Paper Generator

Online Exam Module