Two vectors A = 3 and B = 4 are perpendicular. Resultant of both these vectors is R. The projection of the vector B on the vector R is

Question

Two vectors A = 3 and B = 4 are perpendicular. Resultant of both these vectors is R. The projection of the vector B on the vector R is (A) 3.2 (B) 2.4 (C) 5 (D) 1.25

Tardigrade Admin · Accepted Answer

Here, | A |=3,| B |=4 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/c4e7f369aa1bb83956f1efe97239e711-.png" /> Let angle E O P=φ, then B =R cos φ=4 and A =R sin φ=3 ∴ tan φ=(3/4) Now, cos φ=(4/5) Projection of B on O P is | B | cos φ i.e. 4 cos φ=4 × (4/5)=(16/5)=3.2

Q. Two vectors $A = 3$ and $B = 4$ are perpendicular. Resultant of both these vectors is $R$ . The projection of the vector $B$ on the vector $R$ is

$3.2$

$2.4$

$5$

$1.25$

Here, $∣ A ∣ = 3, ∣ B ∣ = 4$

Let $∠ EOP = ϕ$ , then
$B = R cos ϕ = 4$ and $A = R sin ϕ = 3$
$∴ tan ϕ = \frac{3}{4}$
Now, $cos ϕ = \frac{4}{5}$
Projection of $B$ on $OP$ is $∣ B ∣ cos ϕ$
i.e. $4 cos ϕ = 4 \times \frac{4}{5} = \frac{16}{5} = 3.2$

Q. Two vectors A=3 and B=4 are perpendicular. Resultant of both these vectors is R. The projection of the vector B on the vector R is

3.2

2.4

5

1.25

Here, ∣A∣=3,∣B∣=4 Let ∠EOP=ϕ, then B=Rcosϕ=4 and A=Rsinϕ=3 ∴tanϕ=43​ Now, cosϕ=54​ Projection of B on OP is ∣B∣cosϕ i.e. 4cosϕ=4×54​=516​=3.2

Q. Two vectors $A = 3$ and $B = 4$ are perpendicular. Resultant of both these vectors is $R$ . The projection of the vector $B$ on the vector $R$ is

$3.2$

$2.4$

$5$

$1.25$

Here, $∣ A ∣ = 3, ∣ B ∣ = 4$

Let $∠ EOP = ϕ$ , then
$B = R cos ϕ = 4$ and $A = R sin ϕ = 3$
$∴ tan ϕ = \frac{3}{4}$
Now, $cos ϕ = \frac{4}{5}$
Projection of $B$ on $OP$ is $∣ B ∣ cos ϕ$
i.e. $4 cos ϕ = 4 \times \frac{4}{5} = \frac{16}{5} = 3.2$