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
Find the direction cosines of the line perpendicular to the lines whose direction ratios are -2, 1,-1 and -3, - 4, 1
Direction cosines of the line passing through the points A (- 4, 2, 3) and B (1, 3, -2) are.........
If l, m, n are the direction cosines of a line, then prove that l2 + m2 + n2 = 1. Hence find the
direction angle of the line with the X axis which makes direction angles of 135° and 45° with Y and Z axes respectively.
Find the vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane `vecr.(hati + 2hatj -5hatk) + 9 = 0`
Show that the line through the points (1, −1, 2) and (3, 4, −2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).
Find the angle between the lines whose direction cosines are given by the equations
2l + 2m − n = 0, mn + ln + lm = 0
Write the ratio in which YZ-plane divides the segment joining P (−2, 5, 9) and Q (3, −2, 4).
If a line makes angles α, β and γ with the coordinate axes, find the value of cos2α + cos2β + cos2γ.
The distance of the point P (a, b, c) from the x-axis is
If P (3, 2, −4), Q (5, 4, −6) and R (9, 8, −10) are collinear, then R divides PQ in the ratio
If a line makes angles 90°, 135°, 45° with the x, y and z axes respectively, find its direction cosines.
Verify whether the following ratios are direction cosines of some vector or not
`1/5, 3/5, 4/5`
Find the direction cosines of a vector whose direction ratios are
1, 2, 3
Find the direction cosines and direction ratios for the following vector
`hat"j"`
Find the direction cosines and direction ratios for the following vector
`hat"i" - hat"k"`
If the direction ratios of a line are 1, 1, 2, find the direction cosines of the line.
The x-coordinate of a point on the line joining the points Q(2, 2, 1) and R(5, 1, –2) is 4. Find its z-coordinate.
P is a point on the line segment joining the points (3, 2, –1) and (6, 2, –2). If x co-ordinate of P is 5, then its y co-ordinate is ______.
Find the coordinates of the image of the point (1, 6, 3) with respect to the line `vecr = (hatj + 2hatk) + λ(hati + 2hatj + 3hatk)`; where 'λ' is a scalar. Also, find the distance of the image from the y – axis.
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 ______.
