Calculate the angle between the two lines.

May 4, 2026Mathematics

ScanSolve AI Answer

May 4, 2026

Answer

(1, 2) + k(1, 2)$.

Step 1: Calculate the angle between the two lines. The first line is given in parametric form: $\vec{r} = (1, 2) + k(1, 2)$ . Its direction vector is $\vec{d_1} = (1, 2)$ . The second line is given by the equation $2x + y + 5 = 0$ . Its normal vector is $\vec{n_2} = (2, 1)$ . The direction vector for the second line can be found by taking $(-B, A)$ from $Ax+By+C=0$ , so $\vec{d_2} = (-1, 2)$ .

The angle $\theta$ between two lines with direction vectors $\vec{d_1

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Calculate the angle between the two lines. The first line is given in parametric form: r = (1, 2) + k(1, 2).

Asked on May 4, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 4, 2026

Step 1: Calculate the angle between the two lines. The first line is given in parametric form: r = (1, 2) + k(1, 2). Its direction vector is d_1 = (1, 2). The second line is given by the equation 2x + y + 5 = 0. Its normal vector is n_2 = (2, 1). The direction vector for the second line can be found by taking (-B, A) from Ax+By+C=0, so d_2 = (-1, 2). The angle between two lines with direction vectors $d_1