Advertisements
Advertisements
प्रश्न
If `vec"a"` is any non-zero vector, then `(vec"a" .hat"i")hat"i" + (vec"a".hat"j")hat"j" + (vec"a".hat"k")hat"k"` equals ______.
उत्तर
If `vec"a"` is any non-zero vector, then `(vec"a" .hat"i")hat"i" + (vec"a".hat"j")hat"j" + (vec"a".hat"k")hat"k"` equals `vec"a"`.
Explanation:
Let `vec"a" = "a"_1hat"i" + "a"_2hat"j" + "a"_3hat"k"`
∴ `vec"a"*hat"i" = ("a"_1hat"i" + "a"_2hat"j" + "a"_3hat"k") * hat"i"`
Similarly, `vec"a" * hat"j" = "a"_2` and `vec"a" * hat"k" = "a"_3`
∴ `(vec"a" * hat"i")*hat"i" + (vec"a" * hat"j")hat"j" + (vec"a" * hat"k")*hat"k" = "a"_1hat"i" + "a"_2hat"j" + "a"_3hat"k" = vec"a"`
Hence, the value of the filler is `vec"a"`.
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 \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] are position vectors of the vertices A, B and C respectively, of a triangle ABC, write the value of \[\overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CA} .\]
If \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then write the value of \[\vec{a} + \vec{b} + \vec{c} .\]
Write the position vector of a point dividing the line segment joining points A and B with position vectors \[\vec{a}\] and \[\vec{b}\] externally in the ratio 1 : 4, where \[\overrightarrow{a} = 2 \hat{i} + 3 \hat{j} + 4 \hat{k} \text{ and }\overrightarrow{b} = - \hat{i} + \hat{j} + \hat{k} .\]
If \[\overrightarrow{a} = \hat{i} + 2 \hat{j} , \vec{b} = \hat{j} + 2 \hat{k} ,\] write a unit vector along the vector \[3 \overrightarrow{a} - 2 \overrightarrow{b} .\]
Write a unit vector in the direction of the sum of the vectors \[\overrightarrow{a} = 2 \hat{i} + 2 \hat{j} - 5 \hat{k}\] and \[\overrightarrow{b} = 2 \hat{i} + \hat{j} - 7 \hat{k}\].
If \[\left| \overrightarrow{a} \right| = 4\] and \[- 3 \leq \lambda \leq 2\], then write the range of \[\left| \lambda \vec{a} \right|\].
If points A (60 \[\hat{i}\] + 3 \[\hat{j}\]), B (40 \[\hat{i}\] − 8 \[\hat{j}\]) and C (a \[\hat{i}\] − 52 \[\hat{j}\]) are collinear, then a is equal to
Find the components along the coordinate axes of the position vector of the following point :
R(–11, –9)
If `|bara|` = 3, `|barb|` = 5, `|barc|` = 7 and `bara + barb + barc = bar0`, then the angle between `bara` and `barb` is ______.
Find the lengths of the sides of the triangle and also determine the type of a triangle:
L (3, -2, -3), M (7, 0, 1), N(1, 2, 1).
Find two unit vectors each of which makes equal angles with bar"u", bar"v" and bar"w" where bar"u" = 2hat"i" + hat"j" - 2hat"k", bar"v" = hat"i" + 2hat"j" - 2hat"k", bar"w" = 2hat"i" - 2hat"j" + hat"k".
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"|. (bar"b" + bar"c")`
Using vectors, prove that cos (A – B) = cosA cosB + sinA sinB.
The area of the parallelogram whose adjacent sides are `hat"i" + hat"k"` and `2hat"i" + hat"j" + hat"k"` is ______.
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"`
If `vec"a" = hat"i" + hat"j" + 2hat"k"` and `hat"b" = 2hat"i" + hat"j" - 2hat"k"`, find the unit vector in the direction of `2vec"a" - vec"b"`
Using vectors, find the value of k such that the points (k, – 10, 3), (1, –1, 3) and (3, 5, 3) are collinear.
Classify the following measures as scalar and vector.
10-19 coulomb
Classify the following as scalar and vector quantity.
Work done
Four vectors `veca, vecb, vecc` and `vecx` satisfy the relation `(veca.vecx)vecb = vecc + vecx` where `vecb * veca` ≠ 1. The value of `vecx` in terms of `veca, vecb` and `vecc` is equal to
If two or more vectors are parallel to the same line, such vectors are known as:
The angles of a triangle, two of whose sides are represented by the vectors `sqrt(3)(veca xx vecb)` and `vecb - (veca.vecb)veca` where `vecb` is a non-zero vector and `veca` is a unit vector are ______.
Evaluate the following.
`int x^3/(sqrt1 + x^4) `dx
