Question

16. If a = 31 +1 +2k and b = 21-2; +4k
(a) find the magnitude of axb
(b) find a unit vector perpendicular to both ā and b
(c)find the cosine and sine of the angle between the vector and b​

Answer 1

Steps :

is that a=3i+j+2k, and b=2i-2j+4 ?

well,

Q.a

a × b = i (1·4 - 2·(-2)) - j (3·4 - 2·2) + k (3·(-2) - 1·2)

= i (4 + 4) - j (12 - 4) + k (-6 - 2)

= 8( i-j-k)

(ans of Q.a)

Q.b

unit vector perpendicular to both ā and b is=

$\frac{ a \times b }{ |a \times b| }$

$\frac{8( i-j-k)}{ \sqrt{64 + 64 + 64} }$

$\frac{8( i-j-k)}{ {8 \sqrt{3} } }$

$\frac{( i-j-k)}{ { \sqrt{3} } }$

(ans of Q.b)

Q.c

cos angle between the vector a and b :

$\cos \alpha = \frac{a.b}{ |a| . |b| }$

{calculate steps }

(ans of Q.c)

sine angle between the vector a and b :

$\sin \alpha = \frac{ |a \times b| }{ |a| . |b| }$

{calculate steps }

(ans of Q.c)

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