Advertisements
Advertisements
प्रश्न
Write a unit vector in the direction of \[\overrightarrow{b} = 2 \hat{i} + \hat{j} + 2 \hat{k}\].
उत्तर
Given: \[\overrightarrow{b} = 2 \hat{i} + \hat{j} + 2 \hat{k}\]
\[\left| \overrightarrow{b} \right| = \sqrt{2^2 + 1^2 + 2^2} = \sqrt{4 + 1 + 4} = \sqrt{9} = 3\]
∴ Unit vector = \[\frac{\overrightarrow{b}}{\left| \overrightarrow{b} \right|} = \frac{1}{3}\left( 2 \hat{i} + \hat{j} + 2 \hat{k} \right) = \frac{2}{3} \hat{i} + \frac{1}{3} \stackrel\frown{j} + \frac{2}{3} \hat{k}\]
APPEARS IN
संबंधित प्रश्न
if `veca = 2hati - hatj - 2hatk " and " vecb = 7hati + 2hatj - 3hatk`, , then express `vecb` in the form of `vecb = vec(b_1) + vec(b_2)`, where `vec(b_1)` is parallel to `veca` and `vec(b_2)` is perpendicular to `veca`
If \[\vec{a}\] and \[\vec{b}\] are two non-collinear vectors such that \[x \vec{a} + y \vec{b} = \vec{0} ,\] then write the values of x and y.
If G denotes the centroid of ∆ABC, then write the value of \[\overrightarrow{GA} + \overrightarrow{GB} + \overrightarrow{GC} .\]
If D, E, F are the mid-points of the sides BC, CA and AB respectively of a triangle ABC, write the value of \[\overrightarrow{AD} + \overrightarrow{BE} + \overrightarrow{CF} .\]
If \[\overrightarrow{a} = \hat{i} + 2 \hat{j} , \vec{b} = \hat{j} + 2 \hat{k} ,\] write a unit vector along the vector \[3 \overrightarrow{a} - 2 \overrightarrow{b} .\]
If \[\overrightarrow{a} = \hat{i} + 2 \hat{j} - 3 \hat{k} \text{ and }\overrightarrow{b} = 2 \hat{i} + 4 \hat{j} + 9 \hat{k} ,\] find a unit vector parallel to \[\overrightarrow{a} + \overrightarrow{b}\].
Find the position vector of the mid-point of the line segment AB, where A is the point (3, 4, −2) and B is the point (1, 2, 4).
Find a unit vector in the direction of the vector \[\overrightarrow{a} = 3 \hat{i} - 2 \hat{j} + 6 \hat{k}\].
If \[\left| \overrightarrow{a} \right| = 4\] and \[- 3 \leq \lambda \leq 2\], then write the range of \[\left| \lambda \vec{a} \right|\].
If G is the intersection of diagonals of a parallelogram ABCD and O is any point, then \[O \vec{A} + O \vec{B} + O \vec{C} + O \vec{D} =\]
Find the components along the coordinate axes of the position vector of the following point :
Q(–5, 1)
If `veca` and `vecb` are non- collinear vectors, find the value of x such that the vectors `barα = (x - 2)veca + vecb` and `barβ = (3+2x)bara - 2barb` are collinear.
The vector `bar"a"` is directed due north and `|bar"a"|` = 24. The vector `bar"b"` is directed due west and `|bar"b"| = 7`. Find `|bar"a" + bar"b"|`.
ABCDEF is a regular hexagon. Show that `bar"AB" + bar"AC" + bar"AD" + bar"AE" + bar"AF" = 6bar"AO"`, where O is the centre of the hexagon.
Find a vector in the direction of `bara = hati - 2hatj` that has magnitude 7 units.
Express `- hat"i" - 3hat"j" + 4hat"k"` as the linear combination of the vectors `2hat"i" + hat"j" - 4hat"k", 2hat"i" - hat"j" + 3hat"k"` and `3hat"i" + hat"j" - 2hat"k"`
Select the correct option from the given alternatives:
The volume of tetrahedron whose vectices are (1,-6,10), (-1, -3, 7), (5, -1, λ) and (7, -4, 7) is 11 cu units, then the value of λ is
Find the component form of `bar"a"` if it lies in YZ-plane makes 60° with positive Y-axis and `|bar"a"| = 4`.
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".`
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" 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".(bar"b".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"`
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"`
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")`
lf `overlinea`, `overlineb` and `overlinec` are unit vectors such that `overlinea + overlineb + overlinec = overline0` and angle between `overlinea` and `overlineb` is `pi/3`, then `|overlinea xx overlineb| + |overlineb xx overlinec| + |overlinec xx overlinea|` = ______
If `|vec"a"|` = 8, `|vec"b"|` = 3 and `|vec"a" xx vec"b"|` = 12, then value of `vec"a" * vec"b"` is ______.
Find the unit vector in the direction of the sum of the vectors `vec"a" = 2hat"i" - hat"j" + hat"k"` and `vec"b" = 2hat"j" + hat"k"`.
The vector `vec"a" + vec"b"` bisects the angle between the non-collinear vectors `vec"a"` and `vec"b"` if ______.
The formula `(vec"a" + vec"b")^2 = vec"a"^2 + vec"b"^2 + 2vec"a" xx vec"b"` is valid for non-zero vectors `vec"a"` and `vec"b"`
Classify the following as scalar and vector quantity.
Distance
Check whether the vectors `2hati + 2hatj + 3hatk, - 3hati + 3hatj +2 hatk and 3hati + 4hatk` from a triangle or not.
If `hata` is unit vector and `(2vecx - 3hata)*(2vecx + 3hata)` = 91, find the value of `|vecx|`.
Check whether the vectors `2hati+2hatj+3hatk,-3hati+3hatj+2hatk` and `3hati+4hatk` form a triangle or not.
In the triangle PQR, `bar(PQ)=2bara` and `bar(QR)=2barb`. The mid-point of PR is M. Find following vectors in terms of `bara and barb`.
(i) `bar(PR)` (ii) `bar(PM)` (iii) `bar(QM)`
Check whether the vectors `2hati + 2hatj + 3hatk, -3hati + 3hatj + 2hatk and 3hati + 4hatk` form a triangle or not.
Consider the following statements and choose the correct option:
Statement 1: If `veca` and `vecb` represents two adjacent sides of a parallelogram then the diagonals are represented by `veca + vecb` and `veca - vecb`.
Statement 2: If `veca` and `vecb` represents two diagonals of a parallelogram then the adjacent sides are represented by `2(veca + vecb)` and `2(veca - vecb)`.
Which of the following is correct?
In the triangle PQR, `bar(PQ)` = 2`bara` and `bar(QR)` = 2`barb`. The midpoint of PR is M. Find the following vectors in terms of `bara` and `barb`.
(i) `bar(PR)` (ii) `bar(PM)` (iii) `bar(QM)`
