If α is the angle between two vectors barP=3 hati+4 hatj- hatk and barq=2 hati- hatj+ hatk then, sin (α)=

Question

If α is the angle between two vectors barP=3 hati+4 hatj- hatk and barq=2 hati- hatj+ hatk then, sin (α)= (A) √145 / 156 (B) √135 / 156 (C) √155 / 156 (D) √165 / 156

Tardigrade Admin · Accepted Answer

If α is an acute angle between vectors p and q, then textSin α=(|p × q|/|p| q mid)=(√(4-1)2+(-3-2)2+(-3-8)2/√9+16+1 √4+1+1) =(√9+25+121/√156) =√(155/156)

Q. If $α$ is the angle between two vectors $\overset{ˉ}{P} = 3 \hat{i} + 4 \hat{j} - \hat{k}$ and $\overset{q}{ˉ} = 2 \hat{i} - \hat{j} + \hat{k}$ then, $sin (α) =$

$145/156$

$135/156$

$155/156$

$165/156$

If $α$ is an acute angle between vectors $p$ and $q$ , then
$Sin α = \frac{∣ p \times q ∣}{∣ p ∣ q ∣} = \frac{( 4 - 1 ) ^{2} + ( - 3 - 2 ) ^{2} + ( - 3 - 8 ) ^{2}}{9 + 16 + 1 4 + 1 + 1}$
$= \frac{9 + 25 + 121}{156}$
$= \frac{155}{156}$

Q. If α is the angle between two vectors Pˉ=3i^+4j^​−k^ and qˉ​=2i^−j^​+k^ then, sin(α)=

145/156​

135/156​

155/156​

165/156​