If p -k- and q - ai - b - c k- where a - b - c -2-1-0-1-2- then the number of vectors q perpendicular to p is

P·q=0⇒ a+b+c=0 a=b=c=0,→ number of vectors =1 For unordered pair ( 1,0,1)→ number of vectors =6 For unordered pair ( 2,0,2)→ number of vectors =6 For unordered ...

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Standard XII

Mathematics

Perpendicular Distance of a Point from a Plane

If p =î+ĵ+k̂ ...

Question

If $\to p =^i +^j +^k$ and $\to q = a^i + b^j + c^k,$ where $a, b, c \in {- 2, - 1, 0, 1, 2},$ then the number of vectors $\to q$ perpendicular to $\to p$ is

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Solution

$\to p \cdot \to q = 0 \Rightarrow a + b + c = 0$
$a = b = c = 0, \to number of vectors = 1$
$For unordered pair (- 1, 0, 1) \to number of vectors = 6$
$For unordered pair (- 2, 0, 2) \to number of vectors = 6$
$For unordered pair (- 2, 1, 1) \to number of vectors = 3$
$For unordered pair (- 1, - 1, 2) \to number of vectors = 3$

Hence, total number of vectors $= 1 + 6 + 6 + 3 + 3 = 19$

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If →p=^i+^j+^k and →q=a^i+b^j+c^k, where a,b,c∈{−2,−1,0,1,2}, then the number of vectors →q perpendicular to →p is

If $\to p =^i +^j +^k$ and $\to q = a^i + b^j + c^k,$ where $a, b, c \in {- 2, - 1, 0, 1, 2},$ then the number of vectors $\to q$ perpendicular to $\to p$ is