Q. 65.0( 3 Votes )
A vector is inclined at equal angles to the three axes. If the magnitude of is units, find .
Magnitude of = 2√3
Also, given that
Vector is equally inclined to the three axes.
This means, direction cosines of the unit vector will be same. The direction cosines are (l, m, n).
⇒ l = m = n
The direction cosines of a vector are simply the cosines of the angles between the vector and the three coordinate axes.
We know the relationship between direction cosines is,
l2 + m2 + n2 = 1
⇒ l2 + l2 + l2 = 1 [∵ l = m = n]
⇒ 3.l2 = 1
Also, we know that is represented in terms of direction cosines as,
We are familiar with the formula,
To find ,
Substituting values of and .
Thus, the value of is .
Rate this question :
Write a unit vector in the direction ofMathematics - Board Papers
Fill in the blanks
The values of k for which and is parallel to holds true are _______.Mathematics - Exemplar
A and B are two points with position vectors and respectively. Write the position vector of a point P which divides the line segment AB internally in the ratio 1: 2.Mathematics - Board Papers
L and M are two points with position vectors 2a-b and a+2b respectively. Write the position vector of a point N which divides the line segment LM in the ratio 2:1 externally.Mathematics - Board Papers
The scalar product of the vector with the unit vector along the sum of vectors and is equal to one. Find the value of λ.Mathematics - Board Papers