Recall the definition of the cross product with respect to the unit vectors:
i × i = j × j = k × k = 0
i × j = k
j × k = i
k × i = j
and that the product is anticommutative, so that for any two vectors u and v, we have u × v = - (v × u). (This essentially takes care of part (b).)
Now, given a = 8i + j - 2k and b = 5i - 3j + k, we have
a × b = (8i + j - 2k) × (5i - 3j + k)
a × b = 40 (i × i) + 5 (j × i) - 10 (k × i)
… … … … - 24 (i × j) - 3 (j × j) + 6 (k × j)
… … … … + 8 (i × k) + (j × k) - 2 (k × k)
a × b = - 5 (i × j) - 10 (k × i) - 24 (i × j) - 6 (j × k) - 8 (k × i) + (j × k)
a × b = - 5k - 10j - 24k - 6i - 8j + i
a × b = -5i - 18j - 29k
Answer:
d. It is equal to the component of the gravitational force acting down the ramp.
Explanation:
The stationary crate is inclined at an angle with the horizontal. The Recall, Frictional Force is any Force that opposes motion.
Because the Force of Friction that is opposing the motion of the crate along the inclination side.
Therefore this Frictional force is balanced or equal to the force that is driving the inclined force.
Hence Frictional Force is equal to the Gravitational Force that is acting in the ramp, that is why the crate is stationery.
A = .3*g = 2.94 m/s²
<span>t = v/a = 9/2.94 = 3.061 sec </span>
<span>W = E/t = ½mv²/t = ½*40*9²/3.061 = 529.2 watts</span>
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