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ESSAY sebisanya

36. cos 30° = a.b

|a|.|b|

|b| = a.b

|a| cos 30°

|b| = 15

2√3 × ½√3

|b| = 15

3

|b| = 5 ✔

37. u = (2, –6, 4)

3u = (6, –18, 12)

3u + 2v = 0

3u = –2v

v = 3u

–2

v = (6, –18, 12)

–2

v = (–3, 9, –6) ✔

38. a = (1, 2, 3)

b = (4, –2, 1)

c = (1, –1, –2)

a + p = b + c

p = b + c – a

p = (4+1–1, –2–1–2, 1–2–3)

p = (4, –5, –4) ✔

39. P = (0, 1, 4)

Q = (2, –3, 2)

R = (–1, 0, 2)

PR = (–1–0, 0–1, 2–4)

PR = (–1, –1, –2)

RQ = (2+1, –3–0, 2-2)

RQ = (3, –3, 0)

PR × RQ = (–3+3+0) = 0

|PR| = √([–1]²+[–1]²+[–2]²)

|PR| = √(1+1+4)

|PR| = √6

|RQ| = √(3²+(–3)²+0²)

|RQ| = √(9+9)

|RQ| = √18

|RQ| = 3√2

cos PRQ = PR × RQ

|PR|.|RQ|

cos PRQ = –3+3+0

√6.3√2

cos PRQ = 0

6√3

cos PRQ = 0

PRQ = 90° ✔

40. u = (1, 2, 3)

v = (4, –2, 1)

u.v = 4–4+3

u.v = 3

|v| = √(4²+(–2)²+1²)

|v| = √(16+4+1)

|v| = √21

proyeksi orthogonal vektor ūpadav

= u.v ( 4, –2, 1)

|v|²

= 3 (4i –2j + k)

21

= 4i – 2j + k ✔

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