If p - 3- 5- then 2p- -4p and 1-3 p are respectively a- b- c- d and e- 5-3- Find the value of -a-b-c-d-e

For p = (3, 5) 2p will be obtained by multiply x and y coordinates by 2. i.e., 2p =((3× 2),(5× 2)) =(6,10) Similarly 4p=((3× 4),(5× 4)) =( 12, 20) 1/3p = ...

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Standard XIII

Mathematics

Multiplication of a Vector by a Scalar

If p = 3, 5, ...

Question

If p = (3, 5), then 2p, -4p and $\frac{1}{3}$ p are respectively (a, b), (c, d) and (e, 5/3). Find the value of -(a+b+c+d+e)

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Solution

For p = (3, 5)
2p will be obtained by multiply x and y coordinates by 2.
i.e.,
$2 p = ((3 \times 2), (5 \times 2))$
$= (6, 10)$
Similarly - $4 p = ((3 \times - 4), (5 \times - 4)) = (- 12, - 20) \frac{1}{3} p = ((3 \times \frac{1}{3}), (5 \times \frac{1}{3})) = (1, \frac{5}{3})$
So we get a = 6, b= 10, c = -12, d = -20, e = 1
=> a+b+c+d+e = 6+10-12-20+1
= -15
=> -(a+b+c+d+e) = 15

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If p = (3, 5), then 2p, -4p and 13 p are respectively (a, b), (c, d) and (e, 5/3). Find the value of -(a+b+c+d+e)

For p = (3, 5) 2p will be obtained by multiply x and y coordinates by 2. i.e., 2p=((3×2),(5×2)) =(6,10) Similarly - 4p=((3×−4),(5×−4))=(−12,−20)13p=((3×13),(5×13))=(1,53) So we get a = 6, b= 10, c = -12, d = -20, e = 1 => a+b+c+d+e = 6+10-12-20+1 = -15 => -(a+b+c+d+e) = 15

If p = (3, 5), then 2p, -4p and $\frac{1}{3}$ p are respectively (a, b), (c, d) and (e, 5/3). Find the value of -(a+b+c+d+e)