If hat F =2 hat i + hat j - hat k and hat r =3 hat i +2 hat j -2 hat k , then the scalar and vector products of hat F and hat r have the magnitudes respectively as :

Question

If hat F =2 hat i + hat j - hat k and hat r =3 hat i +2 hat j -2 hat k , then the scalar and vector products of hat F and hat r have the magnitudes respectively as : (A) 5, √3 (B) 4, √5 (C) 10, √2 (D) 10,2

Tardigrade Admin · Accepted Answer

vec F =2 hat i + hat j - hat k vec r =3 hat i +2 hat j -2 hat k vec F ⋅ vec r =6+2+2=10 vec F × vec r =| hat i hat j hat k 2 1 -1 3 2 -2| = hat i (0)- hat j (-1)+ hat k (1) = hat j + hat k | vec F × vec r |=√2

Q. If $\hat{F} = 2 \hat{i} + \hat{j} - \hat{k}$ and $\overset{r}{^} = 3 \hat{i} + 2 \hat{j} - 2 \hat{k}$ , then the scalar and vector products of $\hat{F}$ and $\overset{r}{^}$ have the magnitudes respectively as :

$5, 3$

$4, 5$

$10, 2$

$10, 2$

$F = 2 \hat{i} + \hat{j} - \hat{k}$
$r = 3 \hat{i} + 2 \hat{j} - 2 \hat{k}$
$F \cdot r = 6 + 2 + 2 = 10$
$F \times r = ∣ ∣ \hat{i} 23 \hat{j} 12 \hat{k} - 1 - 2 ∣ ∣$
$= \hat{i} (0) - \hat{j} (- 1) + \hat{k} (1)$
$= \hat{j} + \hat{k}$
$∣ F \times r ∣ = 2$

Q. If F^=2i^+j^​−k^ and r^=3i^+2j^​−2k^, then the scalar and vector products of F^ and r^ have the magnitudes respectively as :

5,3​

4,5​

10,2​

10,2

F=2i^+j^​−k^ r=3i^+2j^​−2k^ F⋅r=6+2+2=10 F×r=∣∣​i^23​j^​12​k^−1−2​∣∣​ =i^(0)−j^​(−1)+k^(1) =j^​+k^ ∣F×r∣=2​

Q. If $\hat{F} = 2 \hat{i} + \hat{j} - \hat{k}$ and $\overset{r}{^} = 3 \hat{i} + 2 \hat{j} - 2 \hat{k}$ , then the scalar and vector products of $\hat{F}$ and $\overset{r}{^}$ have the magnitudes respectively as :

$5, 3$

$4, 5$

$10, 2$

$10, 2$

$F = 2 \hat{i} + \hat{j} - \hat{k}$
$r = 3 \hat{i} + 2 \hat{j} - 2 \hat{k}$
$F \cdot r = 6 + 2 + 2 = 10$
$F \times r = ∣ ∣ \hat{i} 23 \hat{j} 12 \hat{k} - 1 - 2 ∣ ∣$
$= \hat{i} (0) - \hat{j} (- 1) + \hat{k} (1)$
$= \hat{j} + \hat{k}$
$∣ F \times r ∣ = 2$