Advertisements
Advertisements
प्रश्न
If `vec"a" = 2hat"i" + 3hat"j" - 4hat"k", vec"b" = 3hat"i" - 4hat"j" - 5hat"k"`, and `vec"c" = -3hat"i" + 2hat"j" + 3hat"k"`, find the magnitude and direction cosines of `vec"a", vec"b", vec"c"`
Advertisements
उत्तर
`vec"a", vec"b", vec"c" = (2hat"i" + 3hat"j" - 4hat"k") + (3hat"i" - 4hat"j" - 5hat"k") + (-3hat"i" + 2hat"j" + 3hat"k")`
`vec"a", vec"b", vec"c" = 2hat"i" + hat"j" - 6hat"k"`
`|vec"a", vec"b", vec"c"| = |2hat"i" + hat"j" - 6hat"k"|`
= `sqrt(2^2 + 1^2 + (-6)^2`
= `sqrt(4 + 1 + 36)`
= `sqrt(41)`
Direction cosnes of `2hat"i" + hat"j" - 6hat"k"` are
`[2/|2hat"i" + hat"j" - 6hat"k"|, 1/|2hat"i" + hat"j" - 6hat"k"|, (-6)/|2hat"i" + hat"j"- 6hat"k"|]`
`[2/sqrt(41), 1/sqrt(41), (6)/sqrt(41)]`
∴ he magnitde and direction cosines of the vector.
`vec"a" + vec"b" + vec"c"` are `sqrt(41), [2/sqrt(41), 1/sqrt(41), (6)/sqrt(41)]`
APPEARS IN
संबंधित प्रश्न
Direction cosines of the line passing through the points A (- 4, 2, 3) and B (1, 3, -2) are.........
Write the direction ratios of the following line :
`x = −3, (y−4)/3 =( 2 −z)/1`
If the lines `(x-1)/(-3) = (y -2)/(2k) = (z-3)/2 and (x-1)/(3k) = (y-1)/1 = (z -6)/(-5)` are perpendicular, find the value of k.
Find the angle between the vectors whose direction cosines are proportional to 2, 3, −6 and 3, −4, 5.
Find the angle between the lines whose direction ratios are proportional to a, b, c and b − c, c − a, a− b.
Find the angle between the lines whose direction cosines are given by the equations
2l − m + 2n = 0 and mn + nl + lm = 0
If a line has direction ratios proportional to 2, −1, −2, then what are its direction consines?
A rectangular parallelopiped is formed by planes drawn through the points (5, 7, 9) and (2, 3, 7) parallel to the coordinate planes. The length of an edge of this rectangular parallelopiped is
A parallelopiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7), parallel to the coordinate planes. The length of a diagonal of the parallelopiped is
Ratio in which the xy-plane divides the join of (1, 2, 3) and (4, 2, 1) is
If P (3, 2, −4), Q (5, 4, −6) and R (9, 8, −10) are collinear, then R divides PQ in the ratio
Find the direction cosines of the line joining the points P(4,3,-5) and Q(-2,1,-8) .
Find the direction cosines and direction ratios for the following vector
`3hat"i" - 4hat"j" + 8hat"k"`
If a line makes angles `pi/2, 3/4 pi` and `pi/4` with x, y, z axis, respectively, then its direction cosines are ______.
Find the equations of the two lines through the origin which intersect the line `(x - 3)/2 = (y - 3)/1 = z/1` at angles of `pi/3` each.
The area of the quadrilateral ABCD, where A(0,4,1), B(2, 3, –1), C(4, 5, 0) and D(2, 6, 2), is equal to ______.
What will be the value of 'P' so that the lines `(1 - x)/3 = (7y - 14)/(2P) = (z - 3)/2` and `(7 - 7x)/(3P) = (y - 5)/1 = (6 - z)/5` at right angles.
Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is ______.
If a line makes an angle α, β and γ with positive direction of the coordinate axes, then the value of sin2α + sin2β + sin2γ will be ______.
Which identity must be satisfied by the direction cosines \[(l,m,n)\] of a line?
