A vector veca makes equal acute angles on the coordinate axis. Then the projection of vector vec b =5 hat i +7 hat j - hat k on vec a is

Question

A vector veca makes equal acute angles on the coordinate axis. Then the projection of vector vec b =5 hat i +7 hat j - hat k on vec a is (A) (11/15) (B) (11/√3) (C) (4/5) (D) (3/5 √3)

Tardigrade Admin · Accepted Answer

overline a = hat i + hat j + hat k ( overline b ⋅ overline a /| overline a |)=(5+7-1/√3) =(11/√3)

Q. A vector $a$ makes equal acute angles on the coordinate axis. Then the projection of vector $b = 5 \hat{i} + 7 \hat{j} - \hat{k}$ on $a$ is

$\frac{11}{15}$

$\frac{11}{3}$

$\frac{4}{5}$

$\frac{3}{5 3}$

$\overline{a} = \hat{i} + \hat{j} + \hat{k}$
$\frac{b \cdot a}{∣ a ∣} = \frac{5 + 7 - 1}{3}$
$= \frac{11}{3}$

Q. A vector a makes equal acute angles on the coordinate axis. Then the projection of vector b=5i^+7j^​−k^ on a is

1511​

3​11​

54​

53​3​