Question

The two adjacent sides of a parallelogram are 2i - 4j + 5k and i - 2j - 3k. Find the unit vector parallel to one of its diagonals. Also, find its area.

Answer 1

Answer:sukantmishra32

Secondary SchoolMath 13+7 pts

The two adjacent sides of a parallelogram are 2i-4j+5k and i-2j-3k. find the unit vector parallel to its diagonal.also find its area

Report by Artitanwar8009 13.03.2018

Answers

sukantmishra32

Sukantmishra32 · Ambitious

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The unit vector to the diagonal is (3i - 6j + 2k) / 7 and the area of the parallelogram is 11 (5)^0.5

The diagonal of a parallelogram whose adjacent sides a and b are given, is calculated using the formula:

a + b (where both a and b should be in vector notation)

a + b = (i-2j-3k) + (2i-4j+5k)

a + b = 3i - 6j + 2k

Magnitude of a + b is 7

Hence unit vector to the diagonal is (3i - 6j + 2k) / 7

Area of parallelogram is given by formula:

A = 0.5 [a x b]

A = 0.5 [22i + 11j]

A = 11 (5)^0.5

Step-by-step explanation:

Answer 2

Answer: Unit vector say c will be

$\hat{c}=\frac{3\hat{i}-6\hat{j}+2\hat{k}}{7}$

Step-by-step explanation:

Adjacent sides of a parallelogram are given by

2i - 4j + 5k and i - 2j - 3k.

Diagonal of a parallelogram will be

$\vec{c}=(2+1)\hat{i}+(-4-2)\hat{j}+(5-3)\hat{k}\\\\=3\hat{i}-6\hat{j}+2\hat{k}$

Now, we want to find the unit vector parallel to one of its diagonals.

$\hat{c}=\frac{\vec{c}}{\mid c\mid}$

so, magnitude of c is given by

$\mid \vec{c}\mid=\sqrt{3^2+(-6)^2+2^2}\\\\\mid \vec{c}\mid=\sqrt{9+36+4}=\sqrt{49}=7$

so, unit vector say c will be

$\hat{c}=\frac{3\hat{i}-6\hat{j}+2\hat{k}}{7}$