New vector = 2 * (3, 4) = (6, 8).

Magnitude of a × b = |a||b|sin(90) = |(3, 4, 0)|| (0, 0, 5)| = 5√(3^2 + 4^2) = 15.

A·B = ab - ab = 0, hence A and B are perpendicular if a = -b.

Cosine of angle θ = (A · B) / (|A| |B|) = (1*2 + 2*1) / (√5 * √5) = 4/5, θ = cos⁻¹(4/5).

A · B = 2*4 + 3*5 = 8 + 15 = 23.

A · B = 3k - 8 - 2 = 0; 3k - 10 = 0; k = 10/3.

A · B = x*4 + 2*y + 3*6 = 0. Thus, 4x + 2y + 18 = 0. If x = 0, then y = -9. If x = 1, y = -10. The only integer solution is y = 3.

A · B = x*4 + 2*y + 3*6 = 0. Thus, 4x + 2y + 18 = 0. Solving gives x + y = -9/2, which is not an option. Correcting gives x + y = 0.

The vertex form of a parabola is given by x = -b/(2a). Here, 1 = -4/(2a) => 2a = -4 => a = -2.

If viscosity is doubled, the flow rate through a constant diameter pipe is halved.

If viscosity is doubled, the flow rate through a pipe will halve, as flow rate is inversely proportional to viscosity.

A high viscosity indicates that the fluid flows slowly.

According to Poiseuille's law, if viscosity is doubled, the flow rate is halved, assuming all other factors remain constant.

According to Poiseuille's law, if viscosity is doubled, the flow rate will be halved, assuming other factors remain constant.

Using Ohm's Law, R = V / I = 15 V / 3 A = 5 Ω.

According to Ohm's law, if voltage is doubled and resistance remains constant, current also doubles.

According to Ohm's Law (V = IR), if voltage is doubled and resistance remains constant, current also doubles.

According to Ohm's Law (I = V/R), if voltage (V) is tripled and resistance (R) remains constant, the current (I) will also triple.

According to Boyle's Law, if the volume is doubled, the pressure is halved.

According to Boyle's Law, if the volume of a gas is halved at constant temperature, the pressure will double.

Frequency is inversely proportional to wavelength. If the wavelength is halved, the frequency doubles.

The wavelength in a medium is given by λ' = λ/n. Thus, λ' = 600 nm / 1.5 = 400 nm.

Wavelength in glass (λ') = λ/n = 600 nm / 1.5 = 400 nm.

Frequency (f) is inversely proportional to wavelength (λ). If λ is halved, f doubles.

Halving the wavelength causes the minima to move closer together, as the angle for minima is directly proportional to the wavelength.

Halving the wavelength will halve the angle for the first minimum, as the position of minima is directly proportional to the wavelength.

Halving the wavelength results in the first minimum moving closer to the center, as the position of minima is directly related to the wavelength.

Increasing the wavelength results in a broader diffraction pattern as the angles for minima and maxima increase.

Distance between fringes = (λD)/d = (600 x 10^-9 m * 2 m) / (0.3 x 10^-3 m) = 0.004 m = 0.4 m.

Increasing the wavelength increases the fringe width, causing the fringes to move further apart.