Advertisements
Advertisements
प्रश्न
Find a vector `vec"r"` of magnitude `3sqrt(2)` units which makes an angle of `pi/4` and `pi/2` with y and z-axes, respectively.
उत्तर
Here m = `cos pi/4 = 1/sqrt(2)` and n = `cos pi/2` = 0.
Therefore, l2 + m2 + n2 = 1 ...(Gives)
`"l"^2 + 1/2 + 0` = 1
⇒ l = `+- 1/sqrt(2)`
Hence, the required vector `vec"r" = 3sqrt(2) ("l"hat"i" + "m"hat"j" + "n"hat"k")` is given by
`vec"r" = 3sqrt(2) (+- 1/sqrt(2) hat"i" + 1/sqrt(2) hat"j" + 0hat"k")`
= `vec"r" = +- 3hat"i" + 3hat"j"`.
APPEARS IN
संबंधित प्रश्न
If \[\overrightarrow{a}\], \[\overrightarrow{b}\], \[\overrightarrow{c}\] are the position vectors of the vertices of a triangle, then write the position vector of its centroid.
Write a unit vector making equal acute angles with the coordinates axes.
Let G be the centroid of ∆ ABC. If \[\overrightarrow{AB} = \vec{a,} \overrightarrow{AC} = \vec{b,}\] then the bisector \[\overrightarrow{AG} ,\] in terms of \[\vec{a}\text{ and }\vec{b}\] is
If ABCDEF is a regular hexagon, then \[\overrightarrow{AD} + \overrightarrow{EB} + \overrightarrow{FC}\] equals
Select the correct option from the given alternatives:
If `bar"a", bar"b", bar"c"` are non-coplanar unit vectors such that `bar"a"xx (bar"b"xxbar"c") = (bar"b"+bar"c")/sqrt2`, then the angle between `bar"a" "and" bar"b"` is
If `|bar"a"| = |bar"b"| = 1, bar"a".bar"b" = 0, bar"a" + bar"b" + bar"c" = bar"0", "find" |bar"c"|`.
If `bar"a", bar"b", bar"c"` are unit vectors such that `bar"a" + bar"b" + bar"c" = bar0,` then find the value of `bar"a".bar"b" + bar"b".bar"c" + bar"c".bar"a".`
Express `hat"i" + 4hat"j" - 4hat"k"` as the linear combination of the vectors `2hat"i" - hat"j" + 3hat"k", hat"i" - 2hat"j" + 4hat"k"` and `- hat"i" + 3hat"j" - 5hat"k"`.
Show that the vector area of a triangle ABC, the position vectors of whose vertices are `bar"a", bar"b" and bar"c"` is `1/2[bar"a" xx bar"b" + bar"b" xx bar"c" + bar"c" xx bar"a"]`.
Find a unit vector perpendicular to the plane containing the point (a, 0, 0), (0, b, 0) and (0, 0, c). What is the area of the triangle with these vertices?
State whether the expression is meaningful. If not, explain why? If so, state whether it is a vector or a scalar:
`bar"a" xx(bar"b" xx bar"c")`
State whether the expression is meaningful. If not, explain why? If so, state whether it is a vector or a scalar:
`(bar"a" xx bar"b").(bar"c"xxbar"d")`
State whether the expression is meaningful. If not, explain why? If so, state whether it is a vector or a scalar:
`bar"a". bar"b" + bar"c"`
Find the volume of the parallelopiped spanned by the diagonals of the three faces of a cube of side a that meet at one vertex of the cube.
If `bar"a", bar"b", bar"c"` are three non-coplanar vectors show that `(bar"a".(bar"b" xx bar"c"))/((bar"c" xx bar"a").bar"b") + (bar"b".(bar"a" xx bar"c"))/((bar"c" xx bar"a").bar"b") = 0`
For any non-zero vectors a and b, [b a × b a] = ?
If the vectors `xhat"i" - 3hat"j" + 7hat"k" and hat"i" + "y"hat"j" - "z"hat"k"` are collinear then the value of `"xy"^2/"z"` is equal.
Find a vector of magnitude 11 in the direction opposite to that of `vec"PQ"` where P and Q are the points (1, 3, 2) and (–1, 0, 8), respectively.
If `vec"a" = hat"i" + hat"j" + 2hat"k"` and `vec"b" = 2hat"i" + hat"j" - 2hat"k"`, find the unit vector in the direction of `6vec"b"`
Classify the following measures as scalar and vector.
10-19 coulomb
If `veca ≠ vec(0), veca.vecb = veca.vecc, veca xx vecb = veca xx vecc`, then show that `vecb = vecc`.
`bara, barb` and `barc` are three vectors such that `veca + vecb + vecc` 20, `|bara| = 1, |barb| = 2` and `|barc| = 3`. Then `bara. barb + barb.barc + bar(c.a)` is equal to
If two or more vectors are parallel to the same line, such vectors are known as:
In the triangle PQR, `bar(PQ) = 2bara` and `bar(QR)=2barb`. The mid-point of PR is M. Find following vectors in terms of `bar a and bar b `.
- `bar("PR")`
- `bar("PM")`
- `bar("QM")`
Check whether the vectors `2hati + 2hatj + 3hat k, -3hati + 3hatj + 2hat k` and `3hati + 4hatk` form a triangle or not.
Evaluate the following.
`int x^3/(sqrt1 + x^4) `dx
Check whether the vectors `2hati + 2hatj + 3hatk, -3hati + 3hatj + 2hatk and 3hati + 4hatk` form a triangle or not.
Check whether the vectors `2hati + 2hatj + 3hatk, -3hati + 3hatj + 2hatk and 3hati + 4hatk` form a triangle or not.
