Question

JEE MAINS MATHS QUESTION SEPTEMBER 2020,.

Answer 1

If volume of parallelepiped whose coterminous edges are a = i + j + n k, b = 2i + 4j - n k and c = i + n j + 3k is 158

then which of the following is correct ?

1. n = 7
2. n = 9
3. a.c = 17
4. b.c = 10

solution : we know, volume of parallelepiped, v = [a b c ]

⇒158 = $\left|\begin{array}{ccc}1&1&n\\2&4&-n\\1&n&3\end{array}\right|$ for n ≥ 0

⇒158 = 1 (12 + n ²) – (6 + n) + n(2n – 4)

⇒158 = 12 + n² - 6 - n + 2n² - 4n

⇒152 = 3n² - 5n

⇒3n² - 5n - 152 = 0

⇒3n² - 24n + 19n - 152 = 0

⇒n = 8, -38/6 but n ≠ -38/6

so, n = 8

now a.c = (i + j + n k).(i + n j + 3k)

= 1 + n + 3n

= 1 + 4n = 1 + 4 × 8 = 33

b.c = (2i + 4j - n k).(i + n j + 3k)

= 2 + 4n - 3n

= 2 + n

= 2 + 8 = 10

Therefore correct option is (4) b.c = 10

Answer 2

$\huge\bf\underbrace{ANSWER}$

n = 7

n = 9

a.c = 17

b.c = 10

solution : we know, volume of parallelepiped, v = [a b c ]

⇒158 =  for n ≥ 0

⇒158 = 1 (12 + n ²) – (6 + n) + n(2n – 4)

⇒158 = 12 + n² - 6 - n + 2n² - 4n

⇒152 = 3n² - 5n

⇒3n² - 5n - 152 = 0

⇒3n² - 24n + 19n - 152 = 0

⇒n = 8, -38/6 but n ≠ -38/6

so, n = 8

now a.c = (i + j + n k).(i + n j + 3k)

= 1 + n + 3n

= 1 + 4n = 1 + 4 × 8 = 33

b.c = (2i + 4j - n k).(i + n j + 3k)

= 2 + 4n - 3n

= 2 + n

= 2 + 8 = 10

Therefore correct option is (4) b.c = 10

PLEASE MARK ME BRAINLIST ANSWER....