Let u → = 2 i ^ + 3 j ^ + k ^ ,   v → = - 3 i ^ + 2 j ^ and w → = i ^ - j ^ + 4 k ^ ,…

Let u→=2i^+3j^+k^, v→=-3i^+2j^ and w→=i^-j^+4k^, Then which of the following statement is true?
  1. u→ is perpendicular to v→ but not w→
  2. v→ is perpendicular to w→ but not u→
  3. w→ is perpendicular to u→ but not v→
  4. u→ is perpendicular to both v→ and w→

Solution

u→=2i^+3j^+k^, v→=-3i^+2j^, w→=i^-j^+4k^

u→.v→=2i^+3j^+k^.-3i^+2j^

⇒u→.v→=-6+6+0

⇒u→.v→=0  

Therefore. u→ is perpendicular to v→.

Now, u→.w→=(2i^.i^)+(3j^.-j^)+(k^.4k^)

⇒u→.w→=2-3+4=3

Therefore, u→ is not perpendicular w→.

Now, w→.v→=i^-j^+4k^.-3i^+2j^

⇒w→.v→=-3-2+0=-5

Therefore w→ is not perpendicular v→.

Asked in: AP EAMCET 2021 (20 Aug Shift 1)

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