Let veca=α hati+ hatj- hatk and vecb=2 hati+ hatj-α hatk, α0 . If the projection of veca × vecb on the vector - hat i +2 hat j -2 hat k is 30 , then α is equal to

Question

Let veca=α hati+ hatj- hatk and vecb=2 hati+ hatj-α hatk, α>0 . If the projection of veca × vecb on the vector - hat i +2 hat j -2 hat k is 30 , then α is equal to (A) (15/2) (B) 8 (C) (13/2) (D) 7

Tardigrade Admin · Accepted Answer

veca × vecb=(1-α) hati+(α2-2) hatj+(α-2) hatk Projection of veca × vecb text on - hati+2 hatj-2 hatk =(( veca × vecb) ⋅(- hati+2 hatj-2 hatk)/3)=30 ⇒ 2 α2-α-91=0 ⇒ α=7,-(13/2)

Q. Let $a = α \hat{i} + \hat{j} - \hat{k}$ and $b = 2 \hat{i} + \hat{j} - α \hat{k}, α > 0$ . If the projection of $a \times b$ on the vector $- \hat{i} + 2 \hat{j} - 2 \hat{k}$ is $30$ , then $α$ is equal to

$\frac{15}{2}$

8

$\frac{13}{2}$

7

$a \times b = (1 - α) \hat{i} + (α^{2} - 2) \hat{j} + (α - 2) \hat{k}$
Projection of $a \times b on - \hat{i} + 2 \hat{j} - 2 \hat{k}$
$= \frac{( a \times b ) \cdot ( - i ^ + 2 j ^ - 2 k ^ )}{3} = 30$
$\Rightarrow 2 α^{2} - α - 91 = 0$
$\Rightarrow α = 7, - \frac{13}{2}$

Q. Let a=αi^+j^​−k^ and b=2i^+j^​−αk^,α>0 . If the projection of a×b on the vector −i^+2j^​−2k^ is 30 , then α is equal to

215​

8

213​

7

a×b=(1−α)i^+(α2−2)j^​+(α−2)k^ Projection of a×b on −i^+2j^​−2k^ =3(a×b)⋅(−i^+2j^​−2k^)​=30 ⇒2α2−α−91=0 ⇒α=7,−213​

Q. Let $a = α \hat{i} + \hat{j} - \hat{k}$ and $b = 2 \hat{i} + \hat{j} - α \hat{k}, α > 0$ . If the projection of $a \times b$ on the vector $- \hat{i} + 2 \hat{j} - 2 \hat{k}$ is $30$ , then $α$ is equal to

$\frac{15}{2}$

$\frac{13}{2}$

$a \times b = (1 - α) \hat{i} + (α^{2} - 2) \hat{j} + (α - 2) \hat{k}$
Projection of $a \times b on - \hat{i} + 2 \hat{j} - 2 \hat{k}$
$= \frac{( a \times b ) \cdot ( - i ^ + 2 j ^ - 2 k ^ )}{3} = 30$
$\Rightarrow 2 α^{2} - α - 91 = 0$
$\Rightarrow α = 7, - \frac{13}{2}$