Magnitude of A Vector (Copy)
1.
Find the magnitude of vector (3,4).
2.
Find the magnitude of vector (5,12).
3.
Find the magnitude of vector (−8,6).
4.
Find the magnitude of vector (7,−24).
5.
Find the magnitude of vector (−15,20).
6.
The vector from A(2,3) to B(7,11) is AB. Find |AB|.
7.
Find the magnitude of vector from P(−4,6) to Q(5,−2).
8.
Find the length of diagonal of rectangle 8 cm by 15 cm using vector magnitude.
9.
Find the distance between (−3,4) and (4,−3).
10.
Find the distance between (7,−5) and (−2,3).
11.
Find the magnitude of vector (0,−9).
12.
Find the magnitude of vector (−12,0).
13.
A square has side 10 cm. Find the length of its diagonal.
14.
A triangle has vertices A(0,0), B(6,0), C(6,8). Find |AC|.
15.
Find the magnitude of vector (1,1).
16.
Find the magnitude of vector (−7,−24).
17.
Find the magnitude of vector (9,−40).
18.
Find the magnitude of vector (20,21).
19.
Find the distance between (2,−3) and (−4,5).
20.
Find the distance between (−10,6) and (14,−2).
21.
Find the magnitude of vector (12,16).
22.
Find the magnitude of vector (−5,−12).
23.
Find the length of diagonal of a cuboid base 9 cm by 12 cm (use vector in 2D).
24.
Find the magnitude of vector (15,8).
25.
Find the distance between (7,7) and (−7,−7).
26.
Find the magnitude of vector (−9,12).
27.
Find the magnitude of vector (24,−7).
28.
Find the magnitude of vector (−1,−1).
29.
Find the magnitude of vector (50,120).
30.
Find the distance between points A(−6,8) and B(9,−12).
1.
|(3,4)| = √(3²+4²) = √(9+16) = √25 = 5.
2.
|(5,12)| = √(25+144) = √169 = 13.
3.
|(−8,6)| = √(64+36) = √100 = 10.
4.
|(7,−24)| = √(49+576) = √625 = 25.
5.
|(−15,20)| = √(225+400) = √625 = 25.
6.
AB = (7−2, 11−3) = (5,8).
|AB| = √(25+64) = √89 ≈ 9.43.
7.
PQ = (5−(−4), −2−6) = (9,−8).
|PQ| = √(81+64) = √145 ≈ 12.0.
8.
Diagonal = (8,15).
Length = √(64+225) = √289 = 17 cm.
9.
Vector = (4−(−3), −3−4) = (7,−7).
Length = √(49+49) = √98 ≈ 9.9.
10.
Vector = (−2−7, 3−(−5)) = (−9,8).
Length = √(81+64) = √145 ≈ 12.0.
11.
|(0,−9)| = √(0+81) = 9.
12.
|(−12,0)| = √(144+0) = 12.
13.
Diagonal of square side 10 = √(10²+10²) = √200 = 10√2 ≈ 14.1 cm.
14.
AC = (6−0, 8−0) = (6,8).
|AC| = √(36+64) = √100 = 10.
15.
|(1,1)| = √(1+1) = √2 ≈ 1.41.
16.
|(−7,−24)| = √(49+576) = √625 = 25.
17.
|(9,−40)| = √(81+1600) = √1681 = 41.
18.
|(20,21)| = √(400+441) = √841 = 29.
19.
Vector = (−4−2, 5−(−3)) = (−6,8).
Length = √(36+64) = √100 = 10.
20.
Vector = (14−(−10), −2−6) = (24,−8).
Length = √(576+64) = √640 ≈ 25.3.
21.
|(12,16)| = √(144+256) = √400 = 20.
22.
|(−5,−12)| = √(25+144) = √169 = 13.
23.
Diagonal = (9,12).
Length = √(81+144) = √225 = 15 cm.
24.
|(15,8)| = √(225+64) = √289 = 17.
25.
Vector = (−7−7, −7−7) = (−14,−14).
Length = √(196+196) = √392 ≈ 19.8.
26.
|(−9,12)| = √(81+144) = √225 = 15.
27.
|(24,−7)| = √(576+49) = √625 = 25.
28.
|(−1,−1)| = √(1+1) = √2 ≈ 1.41.
29.
|(50,120)| = √(2500+14400) = √16900 = 130.
30.
AB = (9−(−6), −12−8) = (15,−20).
|AB| = √(225+400) = √625 = 25.