Question

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Answer 1

Answer:

Given:

The points (1, –1, 2), (3, 4, –2) and (0, 3, 2), (3, 5, 6).

Let us consider AB be the line joining the points, (1, -1, 2) and (3, 4, -2), and CD be the line through the points (0, 3, 2) and (3, 5, 6).

Now,

The direction ratios, a1, b1, c1 of AB are

(3 – 1), (4 – (-1)), (-2 – 2) = 2, 5, -4.

Similarly,

The direction ratios, a2, b2, c2 of CD are

(3 – 0), (5 – 3), (6 – 2) = 3, 2, 4.

Then, AB and CD will be perpendicular to each other, if a1a2 + b1b2 + c1c2 = 0

a1a2 + b1b2 + c1c2 = 2(3) + 5(2) + 4(-4)

= 6 + 10 – 16

= 0

∴ AB and CD are perpendicular to each other.

Explanation:

..Yes..

Answer 2

Answers :

• Pre-Algebra / Elementary Algebra

• Arithmetic mean (average) = Sum of values / Number of values.
• Probability = Target outcomes / Total outcomes.

• Quadratic Formula: x = −b ± √b²-4ac/2a.

• Distance Formula: d=√(x₁ – x₂)² + (y₁ – y₂)²
• Slope Formula: Slope = y₂ – y₁ / x₂ – x₁

• Slope Intercept: y=mx+b.