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The volume of a sphere is increasing at the rate of 8 cm3/s. Find the rate at which its surface area is increasing when the radius of the sphere is 12 cm.

The total cost C(x) associated with the production of x units of an item is given by C(x) = 0.005x3 – 0.02x2 + 30x + 5000. Find the marginal cost when 3 units are produced, where by marginal cost w...

For what values of a⃗ , the vectors 2î – 3ĵ + 4k̂ and aî + 6ĵ – 8k̂ are collinear?

If a unit vector a⃗ makes angle π3 with î, π4 with ĵ and an acute angle θ with k̂, then find the value of θ.

Find the angle between X-axis and the vector î + ĵ + k̂.

Find the angle between X-axis and the vector î + ĵ + k̂.

If a⃗ = 4î – ĵ + k̂ and b⃗ = 2î – 2ĵ + k̂, then find a unit vector parallel to the vector a⃗ +b⃗