The direction cosines of the line which bisec | vedclass

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

Question

(C) The unit vectors along the positive $Y$ and $Z$ axes are $\hat{j} = (0, 1, 0)$ and $\hat{k} = (0, 0, 1)$ respectively.Any vector along the bisecto

Vedclass · Accepted Answer

$0, 1/\sqrt{2}, 1/\sqrt{2}$

Vedclass · Answer

(C) The unit vectors along the positive $Y$ and $Z$ axes are $\hat{j} = (0, 1, 0)$ and $\hat{k} = (0, 0, 1)$ respectively.Any vector along the bisector of the angle between these two axes is given by the sum of these unit vectors: $\vec{v} = \hat{j} + \hat{k} = (0, 1, 1)$.The magnitude of this vector is $|\vec{v}| = \sqrt{0^2 + 1^2 + 1^2} = \sqrt{2}$.The direction cosines are obtained by dividing the components of the vector by its magnitude:$l = 0/\sqrt{2} = 0$,$m = 1/\sqrt{2}$,$n = 1/\sqrt{2}$.Thus,the direction cosines are $(0, 1/\sqrt{2}, 1/\sqrt{2})$.

The direction cosines of the line which bisects the angle between the positive direction of $Y$ and $Z$ axes are

Similar Questions

The distance between two points $P$ and $Q$ is $d$ and the lengths of the projections of $PQ$ on the coordinate planes are $d_1, d_2, d_3$. Then $d_1^2 + d_2^2 + d_3^2 = k d^2$,where $k$ is:

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$, then the angle between them is

Let $A(1,-1,2), B(6,11,2), C(1,2,6)$ be three points. If $l_1, m_1, n_1$ are the direction cosines of $AB$ and $l_2, m_2, n_2$ are the direction cosines of $AC$,then $|l_1 l_2+m_1 m_2+n_1 n_2|=$

If a line makes an angle of $\pi /4$ with the positive direction of both the $x$-axis and $y$-axis,what angle does it make with the positive direction of the $z$-axis?

$A$ line makes an angle of $45^{\circ}$ with the $x$-axis and congruent angles with the $y$ and $z$-axes. Then,the direction cosines of the line are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module