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Find the values of a and b such that the function defined by f(x) = `{(5", if" x <= 2),(ax +b", if" 2 < x < 10),(21", if" x >= 10):}` is a continuous function.
Concept: undefined >> undefined
Show that the function defined by f(x) = cos (x2) is a continuous function.
Concept: undefined >> undefined
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Show that the function defined by f(x) = |cos x| is a continuous function.
Concept: undefined >> undefined
Examine that sin |x| is a continuous function.
Concept: undefined >> undefined
Represent graphically a displacement of 40 km, 30° east of north.
Concept: undefined >> undefined
Classify the following measures as scalar and vector.
10 kg
Concept: undefined >> undefined
Classify the following as scalar and vector quantity.
Time period
Concept: undefined >> undefined
In Figure, identify the following vector.
Coinitial
Concept: undefined >> undefined
Two collinear vectors are always equal in magnitude.
Concept: undefined >> undefined
Two vectors having the same magnitude are collinear.
Concept: undefined >> undefined
Two collinear vectors having the same magnitude are equal.
Concept: undefined >> undefined
Find the direction cosines of the vector `hati + 2hatj + 3hatk`.
Concept: undefined >> undefined
Find the direction cosines of the vector joining the points A (1, 2, -3) and B (-1, -2, 1) directed from A to B.
Concept: undefined >> undefined
Show that the vector `hati + hatj + hatk` is equally inclined to the axes OX, OY, and OZ.
Concept: undefined >> undefined
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are `hati + 2hatj - hatk` and `-hati + hatj + hatk` respectively, externally in the ratio 2:1.
Concept: undefined >> undefined
Find the position vector of the mid point of the vector joining the points P (2, 3, 4) and Q (4, 1, – 2).
Concept: undefined >> undefined
Show that the points A, B and C with position vectors `veca = 3hati - 4hatj - 4hatk`, `vecb = 2hati - hatj + hatk` and `vecc = hati - 3hatj - 5hatk`, respectively form the vertices of a right angled triangle.
Concept: undefined >> undefined
Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of the x-axis.
Concept: undefined >> undefined
Find the value of x for which `x(hati + hatj + hatk)` is a unit vector.
Concept: undefined >> undefined
