A certain vector in the x y -plane has an x -component of 4 m and a y -component of 10 m. It is then rotated in the x y -plane so that its x -component is doubled. Then its new y -component is (approximately)

Question

A certain vector in the x y -plane has an x -component of 4 m and a y -component of 10 m. It is then rotated in the x y -plane so that its x -component is doubled. Then its new y -component is (approximately) (A) 20 m (B) 7.2 m (C) 5.0 m (D) 4.5 m

Tardigrade Admin · Accepted Answer

Here, A =4 i +10 j ∴ | A |=√(4)2+(10)2 =√16+100 =√116 m Now, according to question, A =8 i +n j So, | A |=√(8)2+n2 ∴ √116=√(8)2+n2 squaring both sides 116 =64+n2 or n2 =116-64=52 or n=7.2 m

Q. A certain vector in the $x y$ -plane has an $x$ -component of $4 m$ and a $y$ -component of $10 m$ . It is then rotated in the $x y$ -plane so that its $x$ -component is doubled. Then its new $y$ -component is (approximately)

20 m

7.2 m

5.0 m

4.5 m

Here, $A = 4 i + 10 j$
$∴ ∣ A ∣ = (4)^{2} + (10)^{2} = 16 + 100$
$= 116 m$
Now, according to question,
$A = 8 i + nj$
So, $∣ A ∣ = (8)^{2} + n^{2}$
$∴ 116 = (8)^{2} + n^{2}$
squaring both sides
$116 = 64 + n^{2}$
or $n^{2} = 116 - 64 = 52$
or $n = 7.2 m$

Q. A certain vector in the xy -plane has an x -component of 4m and a y -component of 10m. It is then rotated in the xy -plane so that its x -component is doubled. Then its new y -component is (approximately)