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For given vectors, `veca = 2hati - hatj + 2hatk` and `vecb = -hati + hatj - hatk`, find the unit vector in the direction of the vector `veca +vecb`.
Concept: undefined >> undefined
Find a vector in the direction of vector `5hati - hatj +2hatk` which has a magnitude of 8 units.
Concept: undefined >> undefined
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Show that the direction cosines of a vector equally inclined to the axes OX, OY, and OZ are `pm1/sqrt3, 1/sqrt3, 1/sqrt3`.
Concept: undefined >> undefined
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
`x/a + y/b = 1`
Concept: undefined >> undefined
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y2 = a (b2 – x2)
Concept: undefined >> undefined
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y = a e3x + b e– 2x
Concept: undefined >> undefined
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y = e2x (a + bx)
Concept: undefined >> undefined
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y = ex (a cos x + b sin x)
Concept: undefined >> undefined
Find the particular solution of the differential equation (1 + e2x) dy + (1 + y2) ex dx = 0, given that y = 1 when x = 0.
Concept: undefined >> undefined
Solve the differential equation `ye^(x/y) dx = (xe^(x/y) + y^2)dy, (y != 0)`
Concept: undefined >> undefined
Find a particular solution of the differential equation (x - y) (dx + dy) = dx - dy, given that y = -1, when x = 0. (Hint: put x - y = t)
Concept: undefined >> undefined
The general solution of the differential equation `(y dx - x dy)/y = 0` is ______.
Concept: undefined >> undefined
The general solution of a differential equation of the type `dx/dy + P_1 x = Q_1` is ______.
Concept: undefined >> undefined
The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is ______.
Concept: undefined >> undefined
Using differentials, find the approximate value of the following up to 3 places of decimal
`sqrt(25.3)`
Concept: undefined >> undefined
Using differentials, find the approximate value of the following up to 3 places of decimal
`sqrt(49.5)`
Concept: undefined >> undefined
Using differentials, find the approximate value of the following up to 3 places of decimal
`sqrt(0.6)`
Concept: undefined >> undefined
Using differentials, find the approximate value of the following up to 3 places of decimal
`(0.009)^(1/3)`
Concept: undefined >> undefined
Using differentials, find the approximate value of the following up to 3 places of decimal
`(0.999)^(1/10)`
Concept: undefined >> undefined
Using differentials, find the approximate value of the following up to 3 places of decimal
`(15)^(1/4)`
Concept: undefined >> undefined
