Вправи: 468

468. Знайдіть кут між даними векторами.

cos(a; b) = a• ba•|b|.

1) |a| = 22+02 = 2; |b| = 02+(-1)2 = 1; a • b = 2 • 0 + 0 •

• (–1) = 0;

cos(a; b) = 02•1 = 0; cos(a; b) = 90°;

2) |a| = 22+(23)2 = 4+12 = 4; |b| = 1,52+02 = 1,5;

a • b = 2 • 1,5 + 23 • 0 = 3; cos(a; b) = 34•1,5 = 12; cos(a; b) = 60°;

3) |a| = 62+(-8)2 = 10; |b| = 122+92 = 15;

a • b = 6 • 12 + (–8) • 9 = 72 – 72 = 0;

тоді cos(a; b) = 010•15 = 0; (a; b) = 90°;

4) |a| = 12+12 = 2; |b| = 22+(-2)2 = 22; a • b = –1 • 2 +

+ 1 • (–2) = –4;

cos(a; b) = -42•22 = –1; (a; b) = 180°.