Let vec a =4 hat i +3 hat j and vec b =3 hat i -4 hat j +5 hat k and vec c is a vector such that vec c ⋅( vec a × vec b )+25=0, vec c ⋅( hat i + hat j + hat k )=4 and projection of vec c on vec a is 1 , then the projection of vec c on vec b equals :

Question

Let vec a =4 hat i +3 hat j and vec b =3 hat i -4 hat j +5 hat k and vec c is a vector such that vec c ⋅( vec a × vec b )+25=0, vec c ⋅( hat i + hat j + hat k )=4 and projection of vec c on vec a is 1 , then the projection of vec c on vec b equals : (A) (5/√2) (B) (1/5) (C) (1/√2) (D) (3/√2)

Tardigrade Admin · Accepted Answer

vec a × vec b =15 hat i -20 hat j -25 hat k Let vecc=x hati+y hatj+z hatk ⇒ 15 x-20 y-25 z+25=0 ⇒ 3 x-4 y-5 z=-5 Also x+y+z=4 and ( vec c ⋅ vec a /| vec a |)=1 ⇒ 4 x+3 y=5 ⇒ vecc=2 hati- hatj+3 hatk Projection of vec c or vec b =(25/5 √2)=(5/√2)

Q. Let $a = 4 \hat{i} + 3 \hat{j}$ and $b = 3 \hat{i} - 4 \hat{j} + 5 \hat{k}$ and $c$ is a vector such that $c \cdot (a \times b) + 25 = 0, c \cdot (\hat{i} + \hat{j} + \hat{k}) = 4$ and projection of $c$ on $a$ is 1 , then the projection of $c$ on $b$ equals :

$\frac{5}{2}$

$\frac{1}{5}$

$\frac{1}{2}$

$\frac{3}{2}$

Q. Let a=4i^+3j^​ and b=3i^−4j^​+5k^ and c is a vector such that c⋅(a×b)+25=0,c⋅(i^+j^​+k^)=4 and projection of c on a is 1 , then the projection of c on b equals :

2​5​

51​

2​1​

2​3​

a×b=15i^−20j^​−25k^ Let c=xi^+yj^​+zk^ ⇒15x−20y−25z+25=0 ⇒3x−4y−5z=−5 Also x+y+z=4 and ∣a∣c⋅a​=1⇒4x+3y=5 ⇒c=2i^−j^​+3k^ Projection of c or b=52​25​=2​5​

Q. Let $a = 4 \hat{i} + 3 \hat{j}$ and $b = 3 \hat{i} - 4 \hat{j} + 5 \hat{k}$ and $c$ is a vector such that $c \cdot (a \times b) + 25 = 0, c \cdot (\hat{i} + \hat{j} + \hat{k}) = 4$ and projection of $c$ on $a$ is 1 , then the projection of $c$ on $b$ equals :

$\frac{5}{2}$

$\frac{1}{5}$

$\frac{1}{2}$

$\frac{3}{2}$